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

Gandhi, Raja Rama; Guedes, Edigles

doi:10.18052/www.scipress.com/BMSA.4.31

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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) =∫^2π₀(dψ)/(1 - k^₂sin²ψ), K' = K(k'). τ = iK' / K, q=exp(πiτ).

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Periodical:

Bulletin of Mathematical Sciences and Applications (Volume 4)

Pages:

31-37

DOI:

https://doi.org/10.18052/www.scipress.com/BMSA.4.31

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:

Raja Rama Gandhi, Edigles Guedes

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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.

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

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