Θεώρημα πρώτων αριθμών (Greek Wikipedia)

Analysis of information sources in references of the Wikipedia article "Θεώρημα πρώτων αριθμών" in Greek language version.

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16doi.org

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7ams.org

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7worldcat.org

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4springer.com

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3archive.org

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1ucla.edu

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1acm.org

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1unilim.fr

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acm.org

doi.acm.org

Avigad, Jeremy; Donnelly, Kevin; Gray, David; Raff, Paul (2007-12-01). «A Formally Verified Proof of the Prime Number Theorem». ACM Trans. Comput. Logic 9 (1). doi:10.1145/1297658.1297660. ISSN 1529-3785. http://doi.acm.org/10.1145/1297658.1297660.

ams.org

Newman, D. J. (1980-01-01). «Simple Analytic Proof of the Prime Number Theorem». The American Mathematical Monthly 87 (9): 693–696. doi:10.2307/2321853. MR 0602825. http://www.jstor.org/stable/2321853.
Zagier, D. (1997-01-01). «Newman's Short Proof of the Prime Number Theorem». The American Mathematical Monthly 104 (8): 705–708. doi:10.2307/2975232. MR 1476753. http://www.jstor.org/stable/2975232.
Baas, Nils; Skau, Christian (2008-01-01). «The lord of the numbers, Atle Selberg. On his life and mathematics». Bulletin of the American Mathematical Society 45 (4): 617–649. doi:10.1090/S0273-0979-08-01223-8. ISSN 0273-0979. http://www.ams.org/bull/2008-45-04/S0273-0979-08-01223-8/.
Rosser, Barkley (1941-01-01). «Explicit Bounds for Some Functions of Prime Numbers». American Journal of Mathematics 63 (1): 211–232. doi:10.2307/2371291. MR 0003018. http://www.jstor.org/stable/2371291.
Bach Eric, Shallit, Jefrey (1996). Algorithmic Number Theory. Cambridge: MIT. ISBN 0-262-02405-5. MR 1406794.
Dusart, Pierre (1999-01-01). «The 𝑘^{𝑡ℎ} prime is greater than 𝑘(ln𝑘+lnln𝑘-1) for 𝑘≥2». Mathematics of Computation of the American Mathematical Society 68 (225): 411–415. doi:10.1090/S0025-5718-99-01037-6. ISSN 0025-5718. MR 1620223. http://www.ams.org/mcom/1999-68-225/S0025-5718-99-01037-6/.
Platt, David (2015-01-01). «Computing 𝜋(𝑥) analytically». Mathematics of Computation 84 (293): 1521–1535. doi:10.1090/S0025-5718-2014-02884-6. ISSN 0025-5718. MR 3315519. http://www.ams.org/mcom/2015-84-293/S0025-5718-2014-02884-6/.

archive.org

Hoffman, Paul (1998). The Man Who Loved Only Numbers. New York: Hyperion Books. σελ. 227. ISBN 0786884061.
Ingham, A.E. (1990). The Distribution of Prime Numbers. Cambridge University Press. σελ. 2-5. ISBN 0-521-39789-8.
Guy, Richard K. (2004). Unsolved problems in number theory. Springer-Verlag. σελ. https://zbmath.org/?format=complete&q=an:1058.11001. ISBN 978-0-387-20860-2.

arxiv.org

Dusart, Pierre (22 Απριλίου 2014). Estimates of Some Functions Over Primes without R.H. (PDF).

csuohio.edu

academic.csuohio.edu

Soprounov, Ivan (1998). A short proof of the Prime Number Theorem for arithmetic progressions. Αρχειοθετήθηκε από το πρωτότυπο στις 2016-11-09. https://web.archive.org/web/20161109070841/http://academic.csuohio.edu/soprunov_i/pdf/primes.pdf.

doi.org

dx.doi.org

Pereira, N. Costa (1985-01-01). «A Short Proof of Chebyshev's Theorem». The American Mathematical Monthly 92 (7): 494–495. doi:10.2307/2322510. http://www.jstor.org/stable/2322510.
Nair, M. (1982-01-01). «On Chebyshev-Type Inequalities for Primes». The American Mathematical Monthly 89 (2): 126–129. doi:10.2307/2320934. http://www.jstor.org/stable/2320934.
Newman, D. J. (1980-01-01). «Simple Analytic Proof of the Prime Number Theorem». The American Mathematical Monthly 87 (9): 693–696. doi:10.2307/2321853. MR 0602825. http://www.jstor.org/stable/2321853.
Zagier, D. (1997-01-01). «Newman's Short Proof of the Prime Number Theorem». The American Mathematical Monthly 104 (8): 705–708. doi:10.2307/2975232. MR 1476753. http://www.jstor.org/stable/2975232.
Koch, Helge von (1901-01-01). «Sur la distribution des nombres premiers» (στα γαλλικά). Acta Mathematica 24 (1): 159–182. doi:10.1007/BF02403071. ISSN 0001-5962. http://link.springer.com/article/10.1007/BF02403071.
Schoenfeld, Lowell (1976-01-01). «Sharper Bounds for the Chebyshev Functions $\theta(x)$ and $\psi(x)$. II». Mathematics of Computation 30 (134): 337–360. doi:10.2307/2005976. http://www.jstor.org/stable/2005976.
Selberg, Atle (1949-01-01). «An Elementary Proof of the Prime-Number Theorem». Annals of Mathematics 50 (2): 305–313. doi:10.2307/1969455. http://www.jstor.org/stable/1969455.
Baas, Nils; Skau, Christian (2008-01-01). «The lord of the numbers, Atle Selberg. On his life and mathematics». Bulletin of the American Mathematical Society 45 (4): 617–649. doi:10.1090/S0273-0979-08-01223-8. ISSN 0273-0979. http://www.ams.org/bull/2008-45-04/S0273-0979-08-01223-8/.
Cornaros, C.; Dimitracopoulos, C. (1994-08-01). «The prime number theorem and fragments ofP A» (στα αγγλικά). Archive for Mathematical Logic 33 (4): 265–281. doi:10.1007/BF01270626. ISSN 0933-5846. http://link.springer.com/article/10.1007/BF01270626.
Avigad, Jeremy; Donnelly, Kevin; Gray, David; Raff, Paul (2007-12-01). «A Formally Verified Proof of the Prime Number Theorem». ACM Trans. Comput. Logic 9 (1). doi:10.1145/1297658.1297660. ISSN 1529-3785. http://doi.acm.org/10.1145/1297658.1297660.
Harrison, John (2009-08-19). «Formalizing an Analytic Proof of the Prime Number Theorem» (στα αγγλικά). Journal of Automated Reasoning 43 (3): 243–261. doi:10.1007/s10817-009-9145-6. ISSN 0168-7433. http://link.springer.com/article/10.1007/s10817-009-9145-6.
Granville, Andrew; Martin, Greg (2006-01-01). «Prime Number Races». The American Mathematical Monthly 113 (1): 1–33. doi:10.2307/27641834. http://www.jstor.org/stable/27641834.
Rosser, Barkley (1941-01-01). «Explicit Bounds for Some Functions of Prime Numbers». American Journal of Mathematics 63 (1): 211–232. doi:10.2307/2371291. MR 0003018. http://www.jstor.org/stable/2371291.
Dusart, Pierre (1999-01-01). «The 𝑘^{𝑡ℎ} prime is greater than 𝑘(ln𝑘+lnln𝑘-1) for 𝑘≥2». Mathematics of Computation of the American Mathematical Society 68 (225): 411–415. doi:10.1090/S0025-5718-99-01037-6. ISSN 0025-5718. MR 1620223. http://www.ams.org/mcom/1999-68-225/S0025-5718-99-01037-6/.
Platt, David (2015-01-01). «Computing 𝜋(𝑥) analytically». Mathematics of Computation 84 (293): 1521–1535. doi:10.1090/S0025-5718-2014-02884-6. ISSN 0025-5718. MR 3315519. http://www.ams.org/mcom/2015-84-293/S0025-5718-2014-02884-6/.
Chebolu, Sunil K.; Miná?, Ján (2011-01-01). «Counting Irreducible Polynomials over Finite Fields Using the Inclusion-Exclusion Principle». Mathematics Magazine 84 (5): 369–371. doi:10.4169/math.mag.84.5.369. http://www.jstor.org/stable/10.4169/math.mag.84.5.369.

jstor.org

Pereira, N. Costa (1985-01-01). «A Short Proof of Chebyshev's Theorem». The American Mathematical Monthly 92 (7): 494–495. doi:10.2307/2322510. http://www.jstor.org/stable/2322510.
Nair, M. (1982-01-01). «On Chebyshev-Type Inequalities for Primes». The American Mathematical Monthly 89 (2): 126–129. doi:10.2307/2320934. http://www.jstor.org/stable/2320934.
Newman, D. J. (1980-01-01). «Simple Analytic Proof of the Prime Number Theorem». The American Mathematical Monthly 87 (9): 693–696. doi:10.2307/2321853. MR 0602825. http://www.jstor.org/stable/2321853.
Zagier, D. (1997-01-01). «Newman's Short Proof of the Prime Number Theorem». The American Mathematical Monthly 104 (8): 705–708. doi:10.2307/2975232. MR 1476753. http://www.jstor.org/stable/2975232.
Schoenfeld, Lowell (1976-01-01). «Sharper Bounds for the Chebyshev Functions $\theta(x)$ and $\psi(x)$. II». Mathematics of Computation 30 (134): 337–360. doi:10.2307/2005976. http://www.jstor.org/stable/2005976.
Jørgensen, Bent; Martínez, José Raúl; Tsao, Min (1994-01-01). «Asymptotic Behaviour of the Variance Function». Scandinavian Journal of Statistics 21 (3): 223–243. http://www.jstor.org/stable/4616314.
Selberg, Atle (1949-01-01). «An Elementary Proof of the Prime-Number Theorem». Annals of Mathematics 50 (2): 305–313. doi:10.2307/1969455. http://www.jstor.org/stable/1969455.
Granville, Andrew; Martin, Greg (2006-01-01). «Prime Number Races». The American Mathematical Monthly 113 (1): 1–33. doi:10.2307/27641834. http://www.jstor.org/stable/27641834.
Rosser, Barkley (1941-01-01). «Explicit Bounds for Some Functions of Prime Numbers». American Journal of Mathematics 63 (1): 211–232. doi:10.2307/2371291. MR 0003018. http://www.jstor.org/stable/2371291.
Chebolu, Sunil K.; Miná?, Ján (2011-01-01). «Counting Irreducible Polynomials over Finite Fields Using the Inclusion-Exclusion Principle». Mathematics Magazine 84 (5): 369–371. doi:10.4169/math.mag.84.5.369. http://www.jstor.org/stable/10.4169/math.mag.84.5.369.

springer.com

link.springer.com

Koch, Helge von (1901-01-01). «Sur la distribution des nombres premiers» (στα γαλλικά). Acta Mathematica 24 (1): 159–182. doi:10.1007/BF02403071. ISSN 0001-5962. http://link.springer.com/article/10.1007/BF02403071.
Goldfeld, D. (1 Ιανουαρίου 2004). Chudnovsky, David, επιμ. The Elementary Proof of the Prime Number Theorem: An Historical Perspective. Springer New York. σελίδες 179–192. ISBN 9781461264903.
Cornaros, C.; Dimitracopoulos, C. (1994-08-01). «The prime number theorem and fragments ofP A» (στα αγγλικά). Archive for Mathematical Logic 33 (4): 265–281. doi:10.1007/BF01270626. ISSN 0933-5846. http://link.springer.com/article/10.1007/BF01270626.
Harrison, John (2009-08-19). «Formalizing an Analytic Proof of the Prime Number Theorem» (στα αγγλικά). Journal of Automated Reasoning 43 (3): 243–261. doi:10.1007/s10817-009-9145-6. ISSN 0168-7433. http://link.springer.com/article/10.1007/s10817-009-9145-6.

ucla.edu

math.ucla.edu

Video και διαφάνειες από τη διάλεξη του Τάο για τους πρώτους αριθμούς, UCLA, Ιανουάριος 2007

unilim.fr

Pierre, Dusart (1998). «Autour de la fonction qui compte le nombre de nombres premiers». France. Αρχειοθετήθηκε από το πρωτότυπο στις 6 Μαΐου 2016.

utm.edu

primes.utm.edu

Caldwell, Chris K. (3 Αυγούστου 2010). «"Conditional Calculation of pi(1024)"». Αρχειοθετήθηκε από το πρωτότυπο στις 25 Σεπτεμβρίου 2014.

web.archive.org

Soprounov, Ivan (1998). A short proof of the Prime Number Theorem for arithmetic progressions. Αρχειοθετήθηκε από το πρωτότυπο στις 2016-11-09. https://web.archive.org/web/20161109070841/http://academic.csuohio.edu/soprunov_i/pdf/primes.pdf.
Pierre, Dusart (1998). «Autour de la fonction qui compte le nombre de nombres premiers». France. Αρχειοθετήθηκε από το πρωτότυπο στις 6 Μαΐου 2016.
Caldwell, Chris K. (3 Αυγούστου 2010). «"Conditional Calculation of pi(1024)"». Αρχειοθετήθηκε από το πρωτότυπο στις 25 Σεπτεμβρίου 2014.

worldcat.org

Koch, Helge von (1901-01-01). «Sur la distribution des nombres premiers» (στα γαλλικά). Acta Mathematica 24 (1): 159–182. doi:10.1007/BF02403071. ISSN 0001-5962. http://link.springer.com/article/10.1007/BF02403071.
Baas, Nils; Skau, Christian (2008-01-01). «The lord of the numbers, Atle Selberg. On his life and mathematics». Bulletin of the American Mathematical Society 45 (4): 617–649. doi:10.1090/S0273-0979-08-01223-8. ISSN 0273-0979. http://www.ams.org/bull/2008-45-04/S0273-0979-08-01223-8/.
Cornaros, C.; Dimitracopoulos, C. (1994-08-01). «The prime number theorem and fragments ofP A» (στα αγγλικά). Archive for Mathematical Logic 33 (4): 265–281. doi:10.1007/BF01270626. ISSN 0933-5846. http://link.springer.com/article/10.1007/BF01270626.
Avigad, Jeremy; Donnelly, Kevin; Gray, David; Raff, Paul (2007-12-01). «A Formally Verified Proof of the Prime Number Theorem». ACM Trans. Comput. Logic 9 (1). doi:10.1145/1297658.1297660. ISSN 1529-3785. http://doi.acm.org/10.1145/1297658.1297660.
Harrison, John (2009-08-19). «Formalizing an Analytic Proof of the Prime Number Theorem» (στα αγγλικά). Journal of Automated Reasoning 43 (3): 243–261. doi:10.1007/s10817-009-9145-6. ISSN 0168-7433. http://link.springer.com/article/10.1007/s10817-009-9145-6.
Dusart, Pierre (1999-01-01). «The 𝑘^{𝑡ℎ} prime is greater than 𝑘(ln𝑘+lnln𝑘-1) for 𝑘≥2». Mathematics of Computation of the American Mathematical Society 68 (225): 411–415. doi:10.1090/S0025-5718-99-01037-6. ISSN 0025-5718. MR 1620223. http://www.ams.org/mcom/1999-68-225/S0025-5718-99-01037-6/.
Platt, David (2015-01-01). «Computing 𝜋(𝑥) analytically». Mathematics of Computation 84 (293): 1521–1535. doi:10.1090/S0025-5718-2014-02884-6. ISSN 0025-5718. MR 3315519. http://www.ams.org/mcom/2015-84-293/S0025-5718-2014-02884-6/.

youtube.com

Video και διαφάνειες από τη διάλεξη του Τάο για τους πρώτους αριθμούς, UCLA, Ιανουάριος 2007

zbmath.org

Guy, Richard K. (2004). Unsolved problems in number theory. Springer-Verlag. σελ. https://zbmath.org/?format=complete&q=an:1058.11001. ISBN 978-0-387-20860-2.