6 papers
Extending the unconditional support in an Iwaniec-Luo-Sarnak family
Lucile Devin, Daniel Fiorilli, Anders Södergren
We study the harmonically weighted one-level density of low-lying zeros of -functions in the family of holomorpic newforms of fixed even weight and prime level tending t…
Central values of zeta functions of non-Galois cubic fields
Arul Shankar, Anders Södergren, Nicolas Templier
The Dedekind zeta functions of infinitely many non-Galois cubic fields have negative central values.
Omega results for cubic field counts via lower-order terms in the one-level density
Peter J. Cho, Daniel Fiorilli, Yoonbok Lee +1
In this paper we obtain a precise formula for the -level density of -functions attached to non-Galois cubic Dedekind zeta functions. We find a secondary term which is unique…
Low-lying zeros in families of holomorphic cusp forms: the weight aspect
Lucile Devin, Daniel Fiorilli, Anders Södergren
We study low-lying zeros of -functions attached to holomorphic cusp forms of level and large weight. In this family, the Katz--Sarnak heuristic with orthogonal symmetry type…
On the generalized circle problem for a random lattice in large dimension
Andreas Strömbergsson, Anders Södergren
In this note we study the error term R_{n,L}(x) in the generalized circle problem for a ball of volume x and a random lattice L of large dimension n. Our main result is the followi…
Low-lying zeros of quadratic Dirichlet -functions: Lower order terms for extended support
Daniel Fiorilli, James Parks, Anders Södergren
We study the -level density of low-lying zeros of Dirichlet -functions attached to real primitive characters of conductor at most . Under the Generalized Riemann Hypothesi…