ON THE TRACE FORMULA FOR HECKE OPERATORS ON CONGRUENCE SUBGROUPS

被引：4

作者：

Popa, Alexandru A. ^{[1
]}

机构：

[1] Romanian Acad, Inst Math Simion Stoilow, POB 1-764, RO-014700 Bucharest, Romania

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 146卷 / 07期

关键词：

Trace formula; Hecke operators; holomorphic modular forms; period polynomials; GROUP CO-HOMOLOGY; MODULAR-FORMS; PERIODS;

D O I：

10.1090/proc/13896

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a new, simple proof of the trace formula for Hecke operators on modular forms for finite index subgroups of the modular group. The proof uses algebraic properties of certain universal Hecke operators acting on period polynomials of modular forms, and it generalizes an approach developed by Don Zagier and the author for the modular group. This approach leads to a very simple formula for the trace on the space of cusp forms plus the trace on the space of modular forms. As applications, we investigate what happens when one varies the weight or the level in the trace formula.

引用

页码：2749 / 2764

页数：16

共 15 条

[1]

[Anonymous], 1993, Research into Automorphic Forms and L Functions

[2]

[Anonymous], PUBLICATIONS MATH SO

[3]

[Anonymous], 1993, A tribute to Emil Grosswald: number theory and related analysis

[4]

[Anonymous], 1990, Festschrift in honor of I. I. Piatetski- Shapiro on the occasion of his sixtieth birthday, Part II (Ramat Aviv, 1989)

[5] MODULAR-FORMS IN CHARACTERISTIC-L AND SPECIAL VALUES OF THEIR L-FUNCTIONS [J].

ASH, A ;

STEVENS, G .

DUKE MATHEMATICAL JOURNAL, 1986, 53 (03) :849-868

[6] Combinatorics of traces of Hecke operators [J].

Frechette, S ;

Ono, K ;

Papanikolas, M .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2004, 101 (49) :17016-17020

[7] PERIODS OF MODULAR-FORMS OF ONE VARIABLE AND GROUP CO-HOMOLOGY .3. [J].

HABERLAND, K .

MATHEMATISCHE NACHRICHTEN, 1983, 112 :297-315

[8] ON THE RATIONALITY OF PERIODS OF PRIMITIVE-FORMS [J].

HATADA, K .

ACTA ARITHMETICA, 1981, 40 (01) :9-40

[9] A combinatorial interpretation of Serre's conjecture on modular Galois representations [J].

Herremans, A .

ANNALES DE L INSTITUT FOURIER, 2003, 53 (05) :1287-+

[10]

Merel L., 1994, Lecture Notes in Math, V1585, P59

← 1 2 →