The landscape of L-functions: degree 3 and conductor 1
Paper in 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

Author

David W. Farmer

American Institute of Mathematics

Sally Koutsoliotas

Bucknell University

Stefan Lemurell

Chalmers, Mathematical Sciences, Algebra and geometry

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,

Subject Categories (SSIF 2011)

Computational Mathematics

Other Mathematics

Roots

Basic sciences

DOI

10.1090/conm/796/16007

More information

Latest update

3/19/2025