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On Andrica’s Conjecture, Cramér’s Conjecture, Gaps between Primes and Jacobi Theta Functions III: A Simple Proof for Andrica’s Conjecture

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Abstract:

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 - k2)1/2 is the complementary modulus, K = K(k) =∫0 (dψ)/(1 - k2 sin2ψ), K' = K(k'). τ = iK' / K, q=exp(πiτ).

Info:

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
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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.

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