Omega results for cubic field counts via lower-order terms in the one-level density

DOI10.1017/fms.2022.70OpenAlexW3129618221MaRDI QIDQ5044382

Daniel Fiorilli, Anders Södergren, Yoonbok Lee, Peter Jaehyun Cho

Publication date: 31 October 2022

Published in: Forum of Mathematics, Sigma (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.08077

zbMATH Keywords

\(L\)-functionsDedekind zeta functiongeneralized Riemann hypothesis\(\Omega\)-estimation in cubic fields

Mathematics Subject Classification ID

Cubic and quartic extensions (11R16) Zeta functions and (L)-functions of number fields (11R42) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Other analytic theory (11R47) Relations with random matrices (11M50)

Related Items (1)

The value-distribution of Artin \(L\)-functions associated with cubic fields in conductor aspect

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Davenport-Heilbronn theorems and second order terms
• Secondary terms in counting functions for cubic fields
• One-level density of families of elliptic curves and the Ratios Conjecture
• A unitary test of the Ratios Conjecture
• Error estimates for the Davenport-Heilbronn theorems
• Autocorrelation of ratios of \(L\)-functions
• Lower order terms for the one-level density of elliptic curve \(L\)-functions
• The subconvexity problem for Artin \(L\)-functions
• Low-lying zeros of \(L\)-functions and random matrix theory
• Low-lying zeros of dihedral \(L\)-functions
• Zeros of principal \(L\)-functions and random matrix theory
• Surpassing the ratios conjecture in the 1-level density of Dirichlet \(L\)-functions
• Lower order terms for the one-level density of a symplectic family of Hecke \(L\)-functions
• Dirichlet characters and low-lying zeros of \(L\)-functions
• Low lying zeros of Artin \(L\)-functions
• Sato-Tate theorem for families and low-lying zeros of automorphic \(L\)-functions. Appendix A by Robert Kottwitz, and Appendix B by Raf Cluckers, Julia Gordon and Immanuel Halupczok.
• Density of cubic field discriminants
• A database of number fields
• n-Level Densities of ArtinL-Functions
• Families of L-Functions and Their Symmetry
• An orthogonal test of the L -functions Ratios conjecture
• A Symplectic Test of the L-Functions Ratios Conjecture
• Zeroes of zeta functions and symmetry
• A fast algorithm to compute cubic fields
• Orthogonal and symplectic 𝑛-level densities
• Linear Statistics of Low-Lying Zeros of L-Functions
• One- and two-level densities for rational families of elliptic curves: evidence for the underlying group symmetries
• Low-lying zeros of quadratic Dirichlet L-functions: A transition in the ratios conjecture
• SATO–TATE EQUIDISTRIBUTION OF CERTAIN FAMILIES OF ARTIN -FUNCTIONS
• Low-lying zeros of quadratic Dirichlet -functions: lower order terms for extended support
• Applications of theL-functions ratios conjectures
• Low-lying zeros of elliptic curve L-functions: Beyond the Ratios Conjecture
• Prime Number Races
• Low-lying zeros of families of elliptic curves
• The Density of Abelian Cubic Fields
• Primes in arithmetic progressions
• Low lying zeros of families of \(L\)-functions

This page was built for publication: Omega results for cubic field counts via lower-order terms in the one-level density