Prime number theorem (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Prime number theorem" in English language version.

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25doi.org

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de la Vallée Poussin, Charles-Jean (1896), "Recherches analytiques sur la théorie des nombres premiers.", Annales de la Société scientifique de Bruxelles, 20 B, 21 B, Imprimeur de l'Académie Royale de Belgique: 183–256, 281–352, 363–397, 351–368

ams.org

mathscinet.ams.org

Hoffman, Paul (1998). The Man Who Loved Only Numbers. New York: Hyperion Books. p. 227. ISBN 978-0-7868-8406-3. MR 1666054.
Goldfeld, Dorian (2004). "The elementary proof of the prime number theorem: an historical perspective" (PDF). In Chudnovsky, David; Chudnovsky, Gregory; Nathanson, Melvyn (eds.). Number theory (New York, 2003). New York: Springer-Verlag. pp. 179–192. doi:10.1007/978-1-4419-9060-0_10. ISBN 978-0-387-40655-8. MR 2044518.
Selberg, Atle (1949), "An Elementary Proof of the Prime-Number Theorem", Annals of Mathematics, 50 (2): 305–313, doi:10.2307/1969455, JSTOR 1969455, MR 0029410, S2CID 124153092
Newman, Donald J. (1980). "Simple analytic proof of the prime number theorem". American Mathematical Monthly. 87 (9): 693–696. doi:10.2307/2321853. JSTOR 2321853. MR 0602825.
Zagier, Don (1997). "Newman's short proof of the prime number theorem". American Mathematical Monthly. 104 (8): 705–708. doi:10.2307/2975232. JSTOR 2975232. MR 1476753.
von Koch, Helge (1901). "Sur la distribution des nombres premiers" [On the distribution of prime numbers]. Acta Mathematica (in French). 24 (1): 159–182. doi:10.1007/BF02403071. MR 1554926. S2CID 119914826.
Schoenfeld, Lowell (1976). "Sharper Bounds for the Chebyshev Functions $ϑ (x)$ and $ψ (x)$ . II". Mathematics of Computation. 30 (134): 337–360. doi:10.2307/2005976. JSTOR 2005976. MR 0457374.
Jørgensen, Bent; Martínez, José Raúl; Tsao, Min (1994). "Asymptotic behaviour of the variance function". Scandinavian Journal of Statistics. 21 (3): 223–243. JSTOR 4616314. MR 1292637.
Baas, Nils A.; Skau, Christian F. (2008). "The lord of the numbers, Atle Selberg. On his life and mathematics" (PDF). Bull. Amer. Math. Soc. 45 (4): 617–649. doi:10.1090/S0273-0979-08-01223-8. MR 2434348.
Cornaros, Charalambos; Dimitracopoulos, Costas (1994). "The prime number theorem and fragments of PA" (PDF). Archive for Mathematical Logic. 33 (4): 265–281. doi:10.1007/BF01270626. MR 1294272. S2CID 29171246. Archived from the original (PDF) on 2011-07-21.
Avigad, Jeremy; Donnelly, Kevin; Gray, David; Raff, Paul (2008). "A formally verified proof of the prime number theorem". ACM Transactions on Computational Logic. 9 (1): 2. arXiv:cs/0509025. doi:10.1145/1297658.1297660. MR 2371488. S2CID 7720253.
Harrison, John (2009). "Formalizing an analytic proof of the Prime Number Theorem". Journal of Automated Reasoning. 43 (3): 243–261. CiteSeerX 10.1.1.646.9725. doi:10.1007/s10817-009-9145-6. MR 2544285. S2CID 8032103.
Granville, Andrew; Martin, Greg (2006). "Prime number races" (PDF). American Mathematical Monthly. 113 (1): 1–33. doi:10.2307/27641834. JSTOR 27641834. MR 2202918.
Rosser, Barkley (1941). "Explicit bounds for some functions of prime numbers". American Journal of Mathematics. 63 (1): 211–232. doi:10.2307/2371291. JSTOR 2371291. MR 0003018.
Arias de Reyna, Juan; Toulisse, Jérémy (2013). "The n-th prime asymptotically". Journal de théorie des nombres de Bordeaux. 25 (3): 521–555. arXiv:1203.5413. doi:10.5802/jtnb.847. MR 3179675. Zbl 1298.11093.
Dusart, Pierre (1999). "The $k$ th prime is greater than $k (log k + log log k - 1)$ for $k \geq 2$ ". Mathematics of Computation. 68 (225): 411–415. doi:10.1090/S0025-5718-99-01037-6. MR 1620223.
Platt, David (2015). "Computing $π (x)$ analytically". Mathematics of Computation. 84 (293): 1521–1535. arXiv:1203.5712. doi:10.1090/S0025-5718-2014-02884-6. MR 3315519. S2CID 119174627.

ams.org

Baas, Nils A.; Skau, Christian F. (2008). "The lord of the numbers, Atle Selberg. On his life and mathematics" (PDF). Bull. Amer. Math. Soc. 45 (4): 617–649. doi:10.1090/S0273-0979-08-01223-8. MR 2434348.

archive.org

Hoffman, Paul (1998). The Man Who Loved Only Numbers. New York: Hyperion Books. p. 227. ISBN 978-0-7868-8406-3. MR 1666054.
Gauss, C. F. (1863), Werke, vol. 2 (1st ed.), Göttingen: Teubner, pp. 444–447.

arxiv.org

Kevin Ford (2002). "Vinogradov's Integral and Bounds for the Riemann Zeta Function" (PDF). Proc. London Math. Soc. 85 (3): 565–633. arXiv:1910.08209. doi:10.1112/S0024611502013655. S2CID 121144007.
Timothy Trudgian (February 2016). "Updating the error term in the prime number theorem". Ramanujan Journal. 39 (2): 225–234. arXiv:1401.2689. doi:10.1007/s11139-014-9656-6. S2CID 11013503.
Avigad, Jeremy; Donnelly, Kevin; Gray, David; Raff, Paul (2008). "A formally verified proof of the prime number theorem". ACM Transactions on Computational Logic. 9 (1): 2. arXiv:cs/0509025. doi:10.1145/1297658.1297660. MR 2371488. S2CID 7720253.
Bennett, Michael A.; Martin, Greg; O'Bryant, Kevin; Rechnitzer, Andrew (2018). "Explicit bounds for primes in arithmetic progressions". Illinois J. Math. 62 (1–4): 427–532. arXiv:1802.00085. doi:10.1215/ijm/1552442669. S2CID 119647640.
Lemke Oliver, Robert J.; Soundararajan, Kannan (2016-08-02). "Unexpected biases in the distribution of consecutive primes". Proceedings of the National Academy of Sciences. 113 (31): E4446-54. arXiv:1603.03720. Bibcode:2016PNAS..113E4446L. doi:10.1073/pnas.1605366113. ISSN 0027-8424. PMC 4978288. PMID 27418603.
Dusart, Pierre (2 February 2010). "Estimates of some functions over primes, without R.H.". arXiv:1002.0442 [math.NT].
Arias de Reyna, Juan; Toulisse, Jérémy (2013). "The n-th prime asymptotically". Journal de théorie des nombres de Bordeaux. 25 (3): 521–555. arXiv:1203.5413. doi:10.5802/jtnb.847. MR 3179675. Zbl 1298.11093.
Axler, Christian (2019). "New Estimates for the $n$ th Prime Number". Journal of Integer Sequences. 22 19.4.2. arXiv:1706.03651.
Platt, David (2015). "Computing $π (x)$ analytically". Mathematics of Computation. 84 (293): 1521–1535. arXiv:1203.5712. doi:10.1090/S0025-5718-2014-02884-6. MR 3315519. S2CID 119174627.
Chebolu, Sunil; Mináč, Ján (December 2011). "Counting Irreducible Polynomials over Finite Fields Using the Inclusion $π$ Exclusion Principle". Mathematics Magazine. 84 (5): 369–371. arXiv:1001.0409. doi:10.4169/math.mag.84.5.369. JSTOR 10.4169/math.mag.84.5.369. S2CID 115181186.

bnf.fr

gallica.bnf.fr

Cesàro, Ernesto (1894). "Sur une formule empirique de M. Pervouchine". Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences (in French). 119: 848–849.

books.google.com

de la Vallée Poussin, Charles-Jean (1899), "Sur la fonction ζ(s) de Riemann et le nombre des nombres premiers inférieurs a une limite donnée.", Mémoires couronnés de l'Académie de Belgique, 59, Imprimeur de l'Académie Royale de Belgique: 1–74

cam.ac.uk

cl.cam.ac.uk

Harrison, John (2009). "Formalizing an analytic proof of the Prime Number Theorem". Journal of Automated Reasoning. 43 (3): 243–261. CiteSeerX 10.1.1.646.9725. doi:10.1007/s10817-009-9145-6. MR 2544285. S2CID 8032103.

columbia.edu

math.columbia.edu

Goldfeld, Dorian (2004). "The elementary proof of the prime number theorem: an historical perspective" (PDF). In Chudnovsky, David; Chudnovsky, Gregory; Nathanson, Melvyn (eds.). Number theory (New York, 2003). New York: Springer-Verlag. pp. 179–192. doi:10.1007/978-1-4419-9060-0_10. ISBN 978-0-387-40655-8. MR 2044518.

doi.org

Apostol, Tom M. (1976). Introduction to Analytic Number Theory. Undergraduate Texts in Mathematics (1 ed.). Springer. doi:10.1007/978-1-4757-5579-4. ISBN 978-1-4757-5579-4.
Costa Pereira, N. (August–September 1985). "A Short Proof of Chebyshev's Theorem". American Mathematical Monthly. 92 (7): 494–495. doi:10.2307/2322510. JSTOR 2322510.
Nair, M. (February 1982). "On Chebyshev-Type Inequalities for Primes". American Mathematical Monthly. 89 (2): 126–129. doi:10.2307/2320934. JSTOR 2320934.
Goldfeld, Dorian (2004). "The elementary proof of the prime number theorem: an historical perspective" (PDF). In Chudnovsky, David; Chudnovsky, Gregory; Nathanson, Melvyn (eds.). Number theory (New York, 2003). New York: Springer-Verlag. pp. 179–192. doi:10.1007/978-1-4419-9060-0_10. ISBN 978-0-387-40655-8. MR 2044518.
Selberg, Atle (1949), "An Elementary Proof of the Prime-Number Theorem", Annals of Mathematics, 50 (2): 305–313, doi:10.2307/1969455, JSTOR 1969455, MR 0029410, S2CID 124153092
Erdős, Paul (1949-07-01), "On a new method in elementary number theory which leads to an elementary proof of the prime number theorem" (PDF), Proceedings of the National Academy of Sciences, 35 (7), U.S.A.: National Academy of Sciences: 374–384, Bibcode:1949PNAS...35..374E, doi:10.1073/pnas.35.7.374, PMC 1063042, PMID 16588909
Newman, Donald J. (1980). "Simple analytic proof of the prime number theorem". American Mathematical Monthly. 87 (9): 693–696. doi:10.2307/2321853. JSTOR 2321853. MR 0602825.
Zagier, Don (1997). "Newman's short proof of the prime number theorem". American Mathematical Monthly. 104 (8): 705–708. doi:10.2307/2975232. JSTOR 2975232. MR 1476753.
Kevin Ford (2002). "Vinogradov's Integral and Bounds for the Riemann Zeta Function" (PDF). Proc. London Math. Soc. 85 (3): 565–633. arXiv:1910.08209. doi:10.1112/S0024611502013655. S2CID 121144007.
Timothy Trudgian (February 2016). "Updating the error term in the prime number theorem". Ramanujan Journal. 39 (2): 225–234. arXiv:1401.2689. doi:10.1007/s11139-014-9656-6. S2CID 11013503.
von Koch, Helge (1901). "Sur la distribution des nombres premiers" [On the distribution of prime numbers]. Acta Mathematica (in French). 24 (1): 159–182. doi:10.1007/BF02403071. MR 1554926. S2CID 119914826.
Schoenfeld, Lowell (1976). "Sharper Bounds for the Chebyshev Functions $ϑ (x)$ and $ψ (x)$ . II". Mathematics of Computation. 30 (134): 337–360. doi:10.2307/2005976. JSTOR 2005976. MR 0457374.
Hardy, G. H.; Littlewood, J. E. (1916). "Contributions to the theory of the Riemann zeta-function and the theory of the distribution of primes". Acta Mathematica. 41: 119–196. doi:10.1007/BF02422942.
Baas, Nils A.; Skau, Christian F. (2008). "The lord of the numbers, Atle Selberg. On his life and mathematics" (PDF). Bull. Amer. Math. Soc. 45 (4): 617–649. doi:10.1090/S0273-0979-08-01223-8. MR 2434348.
Cornaros, Charalambos; Dimitracopoulos, Costas (1994). "The prime number theorem and fragments of PA" (PDF). Archive for Mathematical Logic. 33 (4): 265–281. doi:10.1007/BF01270626. MR 1294272. S2CID 29171246. Archived from the original (PDF) on 2011-07-21.
Avigad, Jeremy; Donnelly, Kevin; Gray, David; Raff, Paul (2008). "A formally verified proof of the prime number theorem". ACM Transactions on Computational Logic. 9 (1): 2. arXiv:cs/0509025. doi:10.1145/1297658.1297660. MR 2371488. S2CID 7720253.
Harrison, John (2009). "Formalizing an analytic proof of the Prime Number Theorem". Journal of Automated Reasoning. 43 (3): 243–261. CiteSeerX 10.1.1.646.9725. doi:10.1007/s10817-009-9145-6. MR 2544285. S2CID 8032103.
Bennett, Michael A.; Martin, Greg; O'Bryant, Kevin; Rechnitzer, Andrew (2018). "Explicit bounds for primes in arithmetic progressions". Illinois J. Math. 62 (1–4): 427–532. arXiv:1802.00085. doi:10.1215/ijm/1552442669. S2CID 119647640.
Granville, Andrew; Martin, Greg (2006). "Prime number races" (PDF). American Mathematical Monthly. 113 (1): 1–33. doi:10.2307/27641834. JSTOR 27641834. MR 2202918.
Lemke Oliver, Robert J.; Soundararajan, Kannan (2016-08-02). "Unexpected biases in the distribution of consecutive primes". Proceedings of the National Academy of Sciences. 113 (31): E4446-54. arXiv:1603.03720. Bibcode:2016PNAS..113E4446L. doi:10.1073/pnas.1605366113. ISSN 0027-8424. PMC 4978288. PMID 27418603.
Rosser, Barkley (1941). "Explicit bounds for some functions of prime numbers". American Journal of Mathematics. 63 (1): 211–232. doi:10.2307/2371291. JSTOR 2371291. MR 0003018.
Arias de Reyna, Juan; Toulisse, Jérémy (2013). "The n-th prime asymptotically". Journal de théorie des nombres de Bordeaux. 25 (3): 521–555. arXiv:1203.5413. doi:10.5802/jtnb.847. MR 3179675. Zbl 1298.11093.
Dusart, Pierre (1999). "The $k$ th prime is greater than $k (log k + log log k - 1)$ for $k \geq 2$ ". Mathematics of Computation. 68 (225): 411–415. doi:10.1090/S0025-5718-99-01037-6. MR 1620223.
Platt, David (2015). "Computing $π (x)$ analytically". Mathematics of Computation. 84 (293): 1521–1535. arXiv:1203.5712. doi:10.1090/S0025-5718-2014-02884-6. MR 3315519. S2CID 119174627.
Chebolu, Sunil; Mináč, Ján (December 2011). "Counting Irreducible Polynomials over Finite Fields Using the Inclusion $π$ Exclusion Principle". Mathematics Magazine. 84 (5): 369–371. arXiv:1001.0409. doi:10.4169/math.mag.84.5.369. JSTOR 10.4169/math.mag.84.5.369. S2CID 115181186.

harvard.edu

ui.adsabs.harvard.edu

Erdős, Paul (1949-07-01), "On a new method in elementary number theory which leads to an elementary proof of the prime number theorem" (PDF), Proceedings of the National Academy of Sciences, 35 (7), U.S.A.: National Academy of Sciences: 374–384, Bibcode:1949PNAS...35..374E, doi:10.1073/pnas.35.7.374, PMC 1063042, PMID 16588909
Lemke Oliver, Robert J.; Soundararajan, Kannan (2016-08-02). "Unexpected biases in the distribution of consecutive primes". Proceedings of the National Academy of Sciences. 113 (31): E4446-54. arXiv:1603.03720. Bibcode:2016PNAS..113E4446L. doi:10.1073/pnas.1605366113. ISSN 0027-8424. PMC 4978288. PMID 27418603.

illinois.edu

faculty.math.illinois.edu

Kevin Ford (2002). "Vinogradov's Integral and Bounds for the Riemann Zeta Function" (PDF). Proc. London Math. Soc. 85 (3): 565–633. arXiv:1910.08209. doi:10.1112/S0024611502013655. S2CID 121144007.

jstor.org

Costa Pereira, N. (August–September 1985). "A Short Proof of Chebyshev's Theorem". American Mathematical Monthly. 92 (7): 494–495. doi:10.2307/2322510. JSTOR 2322510.
Nair, M. (February 1982). "On Chebyshev-Type Inequalities for Primes". American Mathematical Monthly. 89 (2): 126–129. doi:10.2307/2320934. JSTOR 2320934.
Selberg, Atle (1949), "An Elementary Proof of the Prime-Number Theorem", Annals of Mathematics, 50 (2): 305–313, doi:10.2307/1969455, JSTOR 1969455, MR 0029410, S2CID 124153092
Newman, Donald J. (1980). "Simple analytic proof of the prime number theorem". American Mathematical Monthly. 87 (9): 693–696. doi:10.2307/2321853. JSTOR 2321853. MR 0602825.
Zagier, Don (1997). "Newman's short proof of the prime number theorem". American Mathematical Monthly. 104 (8): 705–708. doi:10.2307/2975232. JSTOR 2975232. MR 1476753.
Schoenfeld, Lowell (1976). "Sharper Bounds for the Chebyshev Functions $ϑ (x)$ and $ψ (x)$ . II". Mathematics of Computation. 30 (134): 337–360. doi:10.2307/2005976. JSTOR 2005976. MR 0457374.
Jørgensen, Bent; Martínez, José Raúl; Tsao, Min (1994). "Asymptotic behaviour of the variance function". Scandinavian Journal of Statistics. 21 (3): 223–243. JSTOR 4616314. MR 1292637.
Granville, Andrew; Martin, Greg (2006). "Prime number races" (PDF). American Mathematical Monthly. 113 (1): 1–33. doi:10.2307/27641834. JSTOR 27641834. MR 2202918.
Rosser, Barkley (1941). "Explicit bounds for some functions of prime numbers". American Journal of Mathematics. 63 (1): 211–232. doi:10.2307/2371291. JSTOR 2371291. MR 0003018.
Chebolu, Sunil; Mináč, Ján (December 2011). "Counting Irreducible Polynomials over Finite Fields Using the Inclusion $π$ Exclusion Principle". Mathematics Magazine. 84 (5): 369–371. arXiv:1001.0409. doi:10.4169/math.mag.84.5.369. JSTOR 10.4169/math.mag.84.5.369. S2CID 115181186.

maa.org

Zagier, Don (1997). "Newman's short proof of the prime number theorem". American Mathematical Monthly. 104 (8): 705–708. doi:10.2307/2975232. JSTOR 2975232. MR 1476753.

nih.gov

ncbi.nlm.nih.gov

Erdős, Paul (1949-07-01), "On a new method in elementary number theory which leads to an elementary proof of the prime number theorem" (PDF), Proceedings of the National Academy of Sciences, 35 (7), U.S.A.: National Academy of Sciences: 374–384, Bibcode:1949PNAS...35..374E, doi:10.1073/pnas.35.7.374, PMC 1063042, PMID 16588909
Lemke Oliver, Robert J.; Soundararajan, Kannan (2016-08-02). "Unexpected biases in the distribution of consecutive primes". Proceedings of the National Academy of Sciences. 113 (31): E4446-54. arXiv:1603.03720. Bibcode:2016PNAS..113E4446L. doi:10.1073/pnas.1605366113. ISSN 0027-8424. PMC 4978288. PMID 27418603.

pubmed.ncbi.nlm.nih.gov

Erdős, Paul (1949-07-01), "On a new method in elementary number theory which leads to an elementary proof of the prime number theorem" (PDF), Proceedings of the National Academy of Sciences, 35 (7), U.S.A.: National Academy of Sciences: 374–384, Bibcode:1949PNAS...35..374E, doi:10.1073/pnas.35.7.374, PMC 1063042, PMID 16588909
Lemke Oliver, Robert J.; Soundararajan, Kannan (2016-08-02). "Unexpected biases in the distribution of consecutive primes". Proceedings of the National Academy of Sciences. 113 (31): E4446-54. arXiv:1603.03720. Bibcode:2016PNAS..113E4446L. doi:10.1073/pnas.1605366113. ISSN 0027-8424. PMC 4978288. PMID 27418603.

numdam.org

Hadamard, Jacques (1896), "Sur la distribution des zéros de la fonction ζ(s) et ses conséquences arithmétiques.", Bulletin de la Société Mathématique de France, 24, Société Mathématique de France: 199–220, archived from the original on 2024-09-10

psu.edu

citeseerx.ist.psu.edu

Harrison, John (2009). "Formalizing an analytic proof of the Prime Number Theorem". Journal of Automated Reasoning. 43 (3): 243–261. CiteSeerX 10.1.1.646.9725. doi:10.1007/s10817-009-9145-6. MR 2544285. S2CID 8032103.
Soprounov, Ivan (1998). "A short proof of the Prime Number Theorem for arithmetic progressions". Ohio: Cleveland State University. CiteSeerX 10.1.1.179.460.

renyi.hu

Erdős, Paul (1949-07-01), "On a new method in elementary number theory which leads to an elementary proof of the prime number theorem" (PDF), Proceedings of the National Academy of Sciences, 35 (7), U.S.A.: National Academy of Sciences: 374–384, Bibcode:1949PNAS...35..374E, doi:10.1073/pnas.35.7.374, PMC 1063042, PMID 16588909

semanticscholar.org

api.semanticscholar.org

Selberg, Atle (1949), "An Elementary Proof of the Prime-Number Theorem", Annals of Mathematics, 50 (2): 305–313, doi:10.2307/1969455, JSTOR 1969455, MR 0029410, S2CID 124153092
Kevin Ford (2002). "Vinogradov's Integral and Bounds for the Riemann Zeta Function" (PDF). Proc. London Math. Soc. 85 (3): 565–633. arXiv:1910.08209. doi:10.1112/S0024611502013655. S2CID 121144007.
Timothy Trudgian (February 2016). "Updating the error term in the prime number theorem". Ramanujan Journal. 39 (2): 225–234. arXiv:1401.2689. doi:10.1007/s11139-014-9656-6. S2CID 11013503.
von Koch, Helge (1901). "Sur la distribution des nombres premiers" [On the distribution of prime numbers]. Acta Mathematica (in French). 24 (1): 159–182. doi:10.1007/BF02403071. MR 1554926. S2CID 119914826.
Cornaros, Charalambos; Dimitracopoulos, Costas (1994). "The prime number theorem and fragments of PA" (PDF). Archive for Mathematical Logic. 33 (4): 265–281. doi:10.1007/BF01270626. MR 1294272. S2CID 29171246. Archived from the original (PDF) on 2011-07-21.
Avigad, Jeremy; Donnelly, Kevin; Gray, David; Raff, Paul (2008). "A formally verified proof of the prime number theorem". ACM Transactions on Computational Logic. 9 (1): 2. arXiv:cs/0509025. doi:10.1145/1297658.1297660. MR 2371488. S2CID 7720253.
Harrison, John (2009). "Formalizing an analytic proof of the Prime Number Theorem". Journal of Automated Reasoning. 43 (3): 243–261. CiteSeerX 10.1.1.646.9725. doi:10.1007/s10817-009-9145-6. MR 2544285. S2CID 8032103.
Bennett, Michael A.; Martin, Greg; O'Bryant, Kevin; Rechnitzer, Andrew (2018). "Explicit bounds for primes in arithmetic progressions". Illinois J. Math. 62 (1–4): 427–532. arXiv:1802.00085. doi:10.1215/ijm/1552442669. S2CID 119647640.
Platt, David (2015). "Computing $π (x)$ analytically". Mathematics of Computation. 84 (293): 1521–1535. arXiv:1203.5712. doi:10.1090/S0025-5718-2014-02884-6. MR 3315519. S2CID 119174627.
Chebolu, Sunil; Mináč, Ján (December 2011). "Counting Irreducible Polynomials over Finite Fields Using the Inclusion $π$ Exclusion Principle". Mathematics Magazine. 84 (5): 369–371. arXiv:1001.0409. doi:10.4169/math.mag.84.5.369. JSTOR 10.4169/math.mag.84.5.369. S2CID 115181186.

springer.com

link.springer.com

Apostol, Tom M. (1976). Introduction to Analytic Number Theory. Undergraduate Texts in Mathematics (1 ed.). Springer. doi:10.1007/978-1-4757-5579-4. ISBN 978-1-4757-5579-4.
Hardy, G. H.; Littlewood, J. E. (1916). "Contributions to the theory of the Riemann zeta-function and the theory of the distribution of primes". Acta Mathematica. 41: 119–196. doi:10.1007/BF02422942.

stackexchange.com

math.stackexchange.com

"Why is p_n ∼ n ln(n)?". Mathematics Stack Exchange. Retrieved 2024-10-11.

terrytao.wordpress.com

Tao, Terence (10 December 2014). "254A, Notes 2: Complex-analytic multiplicative number theory". Terence Tao's blog.

umontreal.ca

dms.umontreal.ca

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