The landscape of L-functions: degree 3 and conductor 1
Paper i proceeding, 2024

We extend previous lists by numerically computing approximations to many L-functions of degree d = 3, conductor N = 1, and small spectral parameters. We sketch how previous arguments extend to say that for very small spectral parameters there are no such L-functions. Using the case (d, N) = (3, 1) as a guide, we explain how the set of all L-functions with any fixed invariants (d, N) can be viewed as a landscape of points in a (d − 1)-dimensional Euclidean space. We use Plancherel measure to identify the expected density of points for large spectral parameters for general (d, N).
The points from our data are close to the origin and we find that they have smaller density.

functional equation

L-function

Plancherel measure

Maass form

spectral parameters

Författare

David W. Farmer

American Institute of Mathematics

Sally Koutsoliotas

Bucknell University

Stefan Lemurell

Chalmers, Matematiska vetenskaper, Algebra och geometri

David P Roberts

University of Minnesota

Contemporary Mathematics

0271-4132 (ISSN) 1098-3627 (eISSN)

Vol. 796 313-338
978-1-4704-7260-3 (ISBN)

LuCaNT: LMFDB, Computation, and Number Theory
Providence, RI, USA,

Ämneskategorier (SSIF 2011)

Beräkningsmatematik

Annan matematik

Fundament

Grundläggande vetenskaper

DOI

10.1090/conm/796/16007

Mer information

Senast uppdaterat

2025-03-19