6 papers · 1 filter
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…
The Ratios conjecture for real Dirichlet characters and multiple Dirichlet series
Martin Čech
Conrey, Farmer and Zirnbauer introduced a recipe to find asymptotic formulas for the sum of ratios of products of shifted L-functions. These ratios conjectures are very powerful an…
Mean value of real characters using a double Dirichlet series
Martin Čech
We study the double character sum $\sum\limits_{\substack{m\leq X,\\m\odd}}\sum\limits_{\substack{n\leq Y,\\n\odd}}\leg mn$ and its smoothly weighted counterpart. An asymptotic for…