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

David W. Farmer; Sally Koutsoliotas; Stefan Lemurell; David P. Roberts

doi:10.1090/conm/796/16007

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

David W. Farmer
, Sally Koutsoliotas
, Stefan Lemurell
, David P. Roberts

Mathematics (Morris)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

Abstract

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 show 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.

Original language	English (US)
Title of host publication	LuCaNT
Subtitle of host publication	LMFDB, Computation, and Number Theory - Institute for Computational and Experimental Research in Mathematics, ICERM
Editors	John Cremona, John Jones, Jennifer Paulhus, Andrew V Sutherland, John Voight
Publisher	American Mathematical Society
Pages	313-338
Number of pages	26
ISBN (Print)	9781470472603
DOIs	https://doi.org/10.1090/conm/796/16007
State	Published - 2024
Event	LMFDB, Computation, and Number Theory, LuCaNT 2023 - Providence, United States Duration: Jul 10 2023 → Jul 14 2023

Publication series

Name	Contemporary Mathematics
Volume	796
ISSN (Print)	0271-4132
ISSN (Electronic)	1098-3627

Conference

Conference	LMFDB, Computation, and Number Theory, LuCaNT 2023
Country/Territory	United States
City	Providence
Period	7/10/23 → 7/14/23

Bibliographical note

Publisher Copyright:
© 2024, American Mathematical Society. All rights reserved.

Keywords

functional equation
L-function
Maass form
Plancherel measure
spectral parameters

Publisher link

10.1090/conm/796/16007

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Cite this

Farmer, D. W., Koutsoliotas, S., Lemurell, S., & Roberts, D. P. (2024). The landscape of L-functions: degree 3 and conductor 1. In J. Cremona, J. Jones, J. Paulhus, A. V. Sutherland, & J. Voight (Eds.), LuCaNT: LMFDB, Computation, and Number Theory - Institute for Computational and Experimental Research in Mathematics, ICERM (pp. 313-338). (Contemporary Mathematics; Vol. 796). American Mathematical Society. https://doi.org/10.1090/conm/796/16007

The landscape of L-functions: degree 3 and conductor 1. / Farmer, David W.; Koutsoliotas, Sally; Lemurell, Stefan et al.
LuCaNT: LMFDB, Computation, and Number Theory - Institute for Computational and Experimental Research in Mathematics, ICERM. ed. / John Cremona; John Jones; Jennifer Paulhus; Andrew V Sutherland; John Voight. American Mathematical Society, 2024. p. 313-338 (Contemporary Mathematics; Vol. 796).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Farmer, DW, Koutsoliotas, S, Lemurell, S & Roberts, DP 2024, The landscape of L-functions: degree 3 and conductor 1. in J Cremona, J Jones, J Paulhus, AV Sutherland & J Voight (eds), LuCaNT: LMFDB, Computation, and Number Theory - Institute for Computational and Experimental Research in Mathematics, ICERM. Contemporary Mathematics, vol. 796, American Mathematical Society, pp. 313-338, LMFDB, Computation, and Number Theory, LuCaNT 2023, Providence, United States, 7/10/23. https://doi.org/10.1090/conm/796/16007

Farmer DW, Koutsoliotas S, Lemurell S, Roberts DP. The landscape of L-functions: degree 3 and conductor 1. In Cremona J, Jones J, Paulhus J, Sutherland AV, Voight J, editors, LuCaNT: LMFDB, Computation, and Number Theory - Institute for Computational and Experimental Research in Mathematics, ICERM. American Mathematical Society. 2024. p. 313-338. (Contemporary Mathematics). doi: 10.1090/conm/796/16007

Farmer, David W. ; Koutsoliotas, Sally ; Lemurell, Stefan et al. / The landscape of L-functions : degree 3 and conductor 1. LuCaNT: LMFDB, Computation, and Number Theory - Institute for Computational and Experimental Research in Mathematics, ICERM. editor / John Cremona ; John Jones ; Jennifer Paulhus ; Andrew V Sutherland ; John Voight. American Mathematical Society, 2024. pp. 313-338 (Contemporary Mathematics).

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

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