44 citations · 158 across the 15 of their papers we have counts for
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Some Riemann Hypotheses from Random Walks over Primes
Guilherme França, André LeClair
The aim of this article is to investigate how various Riemann Hypotheses would follow only from properties of the prime numbers. To this end, we consider two classes of -functio…
Transcendental equations satisfied by the individual zeros of Riemann , Dirichlet and modular -functions
Guilherme França, André LeClair
We consider the non-trivial zeros of the Riemann -function and two classes of -functions; Dirichlet -functions and those based on level one modular forms. We show that the…
On the validity of the Euler product inside the critical strip
Guilherme França, André LeClair
The Euler product formula relates Dirichlet functions to an infinite product over primes, and is known to be valid for , where it converges absolutely. We prov…
On the zeros of L-functions
Guilherme França, André LeClair
We generalize our recent construction of the zeros of the Riemann -function to two infinite classes of -functions, Dirichlet -functions and those based on level one modula…
Statistical and other properties of Riemann zeros based on an explicit equation for the -th zero on the critical line
Guilherme França, André LeClair
We show that there are an infinite number of Riemann zeros on the critical line, enumerated by the positive integers , whose ordinates can be obtained as the solution…