素数定理 (Japanese Wikipedia)

Analysis of information sources in references of the Wikipedia article "素数定理" in Japanese language version.

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mathscinet.ams.org

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.
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. MR1620223.
von Koch, Helge (1901). “Sur la distribution des nombres premiers [On the distribution of prime numbers]”. Acta Mathematica 24 (1): 159–182. doi:10.1007/BF02403071. MR1554926. https://zenodo.org/record/2347595.

archive.org

Gauss, C. F. (1863), Werke（全集）, 第2巻 (1st ed.), Göttingen: Teubner, pp. 444–447 .

arxiv.org

“Computing π(x) Analytically)”. 2012年7月25日閲覧。
Kevin Ford (2002). “Vinogradov's Integral and Bounds for the Riemann Zeta Function”. Proc. London Math. Soc. 85 (3): 565–633. arXiv:1910.08209. doi:10.1112/S0024611502013655.

csuohio.edu

academic.csuohio.edu

Soprounov, Ivan (1998年). “A short proof of the Prime Number Theorem for arithmetic progressions”. Cleveland State University. 2022年8月7日閲覧。

doi.org

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.
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. MR1620223.
Kevin Ford (2002). “Vinogradov's Integral and Bounds for the Riemann Zeta Function”. Proc. London Math. Soc. 85 (3): 565–633. arXiv:1910.08209. doi:10.1112/S0024611502013655.
von Koch, Helge (1901). “Sur la distribution des nombres premiers [On the distribution of prime numbers]”. Acta Mathematica 24 (1): 159–182. doi:10.1007/BF02403071. MR1554926. https://zenodo.org/record/2347595.
Chebolu, Sunil; Ján Mináč (December 2011). “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.

illinois.edu

faculty.math.illinois.edu

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

jstor.org

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; Ján Mináč (December 2011). “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.

oeis.org

$π$ (x):A006880
Difference between pi(10^n) and the integer nearest to 10^n / log(10^n).:A057835
Difference between nearest integer to Li(10^n) and pi(10^n), where Li(x) = integral of log(x) and pi(10^n) = number of primes <= 10^n:A057752
Integer nearest to 10^n / log(10^n). x:A057834
Integer nearest to Li(10^n), where Li(x) = integral(0..x, dt/log(t)).:A057754

utm.edu

primes.utm.edu

“Conditional Calculation of pi(10²⁴)”. Chris K. Caldwell. 2010年8月4日時点のオリジナルよりアーカイブ。2010年8月3日閲覧。

web.archive.org

“Conditional Calculation of pi(10²⁴)”. Chris K. Caldwell. 2010年8月4日時点のオリジナルよりアーカイブ。2010年8月3日閲覧。

wolfram.com

mathworld.wolfram.com

Weisstein, Eric W. "Gram Series". mathworld.wolfram.com (英語).

zbmath.org

Littlewood, J.E. (1914). “Sur la distribution des nombres premiers”. Comptes Rendus 158: 1869–1872. JFM 45.0305.01.

zenodo.org

von Koch, Helge (1901). “Sur la distribution des nombres premiers [On the distribution of prime numbers]”. Acta Mathematica 24 (1): 159–182. doi:10.1007/BF02403071. MR1554926. https://zenodo.org/record/2347595.