4 papers · 2 filters
First moment of quadratic Dirichlet -functions with secondary terms
Martin Čech
We study the first moment of primitive quadratic Dirichlet -functions. Assuming the Riemann hypothesis and the generalized Lindelöf hypothesis, we obtain an asymptotic formula a…
Low-lying zeros in families of Maass form L-functions: an extended density theorem
Martin Čech, Lucile Devin, Daniel Fiorilli +2
We study the one-level density of low-lying zeros in the family of Maass form -functions of prime level tending to infinity. Generalizing the influential work of Iwaniec, Lu…
Multiple Dirichlet series predictions for moments of -functions: unitary, symplectic and orthogonal examples
Siegfred Baluyot, Martin Čech
We devise heuristics using multiple Dirichlet series to predict asymptotic formulas for shifted moments of (1) the family of Dirichlet -functions of all even primitive character…
On optimality of mollifiers
Martin Čech, Kaisa Matomäki
Mollifiers are used in a variety of contexts, for instance to study the non-vanishing of -functions. In this paper, we study the general question of finding optimal mollifiers a…