Toroidal families and averages of L-functions, I

被引：0

作者：

Fouvry, Etienne ^{[1
]}

Kowalski, Emmanuel ^{[2
]}

Michel, Philippe ^{[3
]}

机构：

[1] Univ Paris Saclay, CNRS, Lab Math Orsay, F-91405 Orsay, France

[2] Swiss Fed Inst Technol, DMATH, CH-8092 Zurich, Switzerland

[3] Ecole Polytech Fed Lausanne, TAN, Stn 8, SB, CH-1015 Lausanne, Switzerland

来源：

ACTA ARITHMETICA | 2024年 / 214卷

关键词：

L-functions; toroidal family; Dirichlet characters; exponential sums over finite fields; toric congruences; moments of L-functions; EXPONENTIAL-SUMS; BILINEAR-FORMS; MOMENTS; VALUES; STRATIFICATION; TWISTS; NUMBER;

D O I：

10.4064/aa230323-24-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We initiate the study of certain families of L-functions attached to characters of subgroups of higher-rank tori, and of their average at the central point. In particular, we evaluate the average of the values L(1/2, chi(a))L(1/2, chi(b)) for arbitrary integers a and b when chi varies over Dirichlet characters of a given prime modulus.

引用

页码：109 / 142

页数：34

共 50 条

[31] P-adic L-functions in universal deformation families
Loeffler, David
ANNALES MATHEMATIQUES DU QUEBEC, 2023, 47 (01): : 117 - 137
[32] Nonvanishing of L-functions, the Ramanujan Conjecture, and Families of Hecke Characters
Blomer, Valentin
Brumley, Farrell
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2013, 65 (01): : 22 - 51
[33] P-adic L-functions in universal deformation families
David Loeffler
Annales mathématiques du Québec, 2023, 47 : 117 - 137
[34] SYMMETRIC POWER L-FUNCTIONS FOR FAMILIES OF GENERALIZED KLOOSTERMAN SUMS
Haessig, C. Douglas
Sperber, Steven
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 369 (02) : 1459 - 1493
[35] The effect of convolving families of L-functions on the underlying group symmetries
Duenez, Eduardo
Miller, Steven J.
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2009, 99 : 787 - 820
[36] p-ADIC L-FUNCTIONS AND THE GEOMETRY OF HIDA FAMILIES
KRAMER-MILLER, Joe
ANNALES DE L INSTITUT FOURIER, 2022, 72 (02) : 727 - 770
[37] A weighted one-level density of families of L-functions
Fazzari, Alessandro
ALGEBRA & NUMBER THEORY, 2024, 18 (01) : 87 - 132
[38] Determining Optimal Test Functions for Bounding the Average Rank in Families of L-Functions
Freeman, Jesse
Miller, Steven J.
SCHOLAR - A SCIENTIFIC CELEBRATION HIGHLIGHTING OPEN LINES OF ARITHMETIC RESEARCH, 2015, 655 : 97 - 116
[39] The Second Moment Theory of Families of L-Functions-The Case of Twisted Hecke L-Functions
Blomer, Valentin
Fouvry, Etienne
Kowalski, Emmanuel
Michel, Philippe
Miliocvic, Djordje
Sawin, Will
MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2023, 282 (1394) : 1 - +
[40] ON L-FUNCTIONS
AYOUB, R
MONATSHEFTE FUR MATHEMATIK, 1967, 71 (03): : 193 - &

← 1 2 3 4 5 →