Spectral Methods And Prime Numbers Counting Problems

Abstract

A recent heuristic argument based on basic concepts in spectral analysis showed that the twin prime conjecture and a few other related primes counting problems are valid. A rigorous version of the spectral method, and a proof of the more general dePolignac conjecture on the existence of infinitely many primes pairs p and p + 2k, k => 1, is proposed in this note.

Thirty Pages. Keywords: Distribution of Primes, Twin Primes Conjecture, dePolignac Conjecture, Germain Primes, Prime Diophantine Equations

References in corpus (4)

• An Amazing Prime Heuristic
• On the error term in a Parseval type formula in the theory of Ramanujan expansions
• Linking the Circle and the Sieve: Ramanujan - Fourier Series
• Some experiments on Bateman-Horn