4 citations · 4 across the 9 of their papers we have counts for
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An identity concerning the Riemann-zeta function
Douglas Azevedo
For a certain function we prove that the identity holds in the half-plane Re and bo…
Zero-free strips for the Riemann zeta-function derived from the Prime Number Theorem
Douglas Azevedo
We use the Prime Number Theorem to prove the existence of zero-free strips for the Riemann-zeta function. Precisely, we prove that there exists for which if then…
Gaps of powers of consecutive primes and some consequences
Douglas Azevedo, Tiago Reis
Let denote the -th prime number, be a sequence of positive numbers and . In this note we prove that the inequality $$q_n p_{n+1}^{x}-q_{n+1}p_{n}…
About de Polignac's conjecture
Douglas Azevedo
In this note we present a method to bound gaps between primes via the divergence of the series of reciprocals of the prime numbers, a consequence of a version of the Bertrand's tes…
Bounds on prime gaps as a consequence of the divergence of the series of reciprocal primes
Douglas Azevedo
In this paper, using the well known fact that the series of reciprocals of primes diverges, we obtain a general inequality for gaps of consecutive primes that holds for infinitely…