4 citations · 4 across the 6 of their papers we have counts for
6 papers · 1 filter
On M-functions associated with modular forms
Philippe Lebacque, Alexey Zykin
Let be a primitive cusp form of weight and level let be a Dirichlet character of conductor coprime with and let denote either $\…
Uniform distribution of zeroes of -functions of modular forms
Alexey Zykin
We prove under GRH that zeros of -functions of modular forms of level and weight become uniformly distributed on the critical line when
On the Number of Rational Points of Jacobians over Finite Fields
Philippe Lebacque, Alexey Zykin
In this article we prove lower and upper bounds for class numbers of algebraic curves defined over finite fields. These bounds turn out to be better than most of the previously kno…
Asymptotic properties of zeta functions over finite fields
Alexey Zykin
In this paper we study asymptotic properties of families of zeta and -functions over finite fields. We do it in the context of three main problems: the basic inequality, the Bra…
Asymptotic properties of Dedekind zeta functions in families of number fields
Alexey Zykin
The main goal of this paper is to prove a formula that expresses the limit behaviour of Dedekind zeta functions for in families of number fields, assuming that the Ge…
On logarithmic derivatives of zeta functions in families of global fields
Philippe Lebacque, Alexey Zykin
We prove a formula for the limit of logarithmic derivatives of zeta functions in families of global fields with an explicit error term. This can be regarded as a rather far reachin…