The highest lowest zero of general L-functions
Artikel i vetenskaplig tidskrift, 2015

Stephen D. Miller showed that, assuming the Generalized Rie-mann Hypothesis, every entire L-function of real archimedeantype has a zero in the interval12+itwith −t0<t <t0, where t0≈14.13 corresponds to the first zero of the Riemann zeta function. We give a numerical example of a self-dual degree-4 L-function whose first positive imaginary zero is at t1≈14.496. In particular, Miller’s result does not hold for general L-functions. We show that all L-functions satisfying some additional (conjecturally true) conditions have a zero in the interval (−t2, t2)with t2≈22.661.

L-function

Zero gap

Zero

Författare

Jonathan Bober

Briam Conrey

David Farmer

Akio Fujii

Sally Koutsoliotas

Stefan Lemurell

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Michael Rubinstein

Hiroyoki Yoshida

Journal of Number Theory

0022-314X (ISSN) 1096-1658 (eISSN)

Vol. 147 364-373

Ämneskategorier

Matematik

Fundament

Grundläggande vetenskaper

DOI

10.1016/j.jnt.2014.07.023

Mer information

Senast uppdaterat

2021-05-25