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We will use the notation of Armitage and Eberlein, [see 1, p. 103]: *k *is a real number such that 0< *k* < 1;* k'* = (1 - *k*^{2})^{1/2} is the complementary modulus, *K *= *K(k*) =∫^{2π}_{0 }(*d*ψ)/(1 - *k*^{2 }sin^{2}*ψ*),* K'* = *K*(*k'*). *τ* =* iK' / K*, *q*=exp(*πiτ).*

Periodical:

Bulletin of Mathematical Sciences and Applications (Volume 4)

Pages:

31-37

Citation:

R. R. Gandhi and E. Guedes, "On Andrica’s Conjecture, Cramér’s Conjecture, Gaps between Primes and Jacobi Theta Functions III: A Simple Proof for Andrica’s Conjecture", Bulletin of Mathematical Sciences and Applications, Vol. 4, pp. 31-37, 2013

Online since:

May 2013

Authors:

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License

References:

[1] Armitage, J. V. and Eberlein, W. F., Elliptic Functions, London Mathematical Society, (2006).

[2] http://en.wikipedia.org/wiki/Prime_number_theorem, available in April 25, (2013).

[3] Prof. Dr. Raja Rama Gandhi and Guedes, Edigles, On Andrica's Conjecture, gaps Between Primes and Jacobi Theta Functions.

DOI: https://doi.org/10.18052/www.scipress.com/bmsa.4.20
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