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D. Zagier (1990)
Hecke operators and periods of modular forms
Alexandru Popa, D. Zagier (2017)
An elementary proof of the Eichler–Selberg trace formulaJournal für die reine und angewandte Mathematik (Crelles Journal), 2020
D Zagier (1993)
Periods of modular forms, traces of Hecke operators, and multiple zeta values. Research into automorphic forms and $$L$$ L -functions (Kyoto, 1992)Sūrikaisekikenkyūsho Kōkyūroku, 843
H Hijikata (1974)
10.2969/jmsj/02610056J. Math. Soc. Jan., 26
Florin Radulescu (2014)
Endomorphisms of spaces of virtual vectors fixed by a discrete groupRussian Mathematical Surveys, 71
(1976)
Trace des opérateurs de Hecke sur 0(N)
Jean-Pierre Serre (1997)
Répartition asymptotique des valeurs propres de l’opérateur de Hecke _Journal of the American Mathematical Society, 10
N. Skoruppa, D. Zagier (1988)
Jacobi forms and a certain space of modular formsInventiones mathematicae, 94
H. Cohen (1975)
Sums involving the values at negative integers of L-functions of quadratic charactersMathematische Annalen, 217
H. Saito (1972)
On Eichler's trace formulaJournal of The Mathematical Society of Japan, 24
Michael Mertens (2013)
Mock modular forms and class number relationsResearch in the Mathematical Sciences, 1
Alexandru Popa, D. Zagier (2016)
A combinatorial refinement of the Kronecker-Hurwitz class number relationarXiv: Number Theory
N. Kaplan, Ian Petrow (2015)
Elliptic curves over a finite field and the trace formulaProceedings of the London Mathematical Society, 115
M. Eichler (1955)
Über die Darstellbarkeit von Modulformen durch Thetareihen.Journal für die reine und angewandte Mathematik (Crelles Journal), 1955
Hirofumi Ishikawa, Y. Ihara (1973)
On the trace formula for Hecke operatorsJournal of the Faculty of Science, the University of Tokyo. Sect. 1 A, Mathematics, 20
D. Zagier (1993)
PERIODS OF MODULAR FORMS, TRACES OF HECKE OPERATORS, AND MULTIPLE ZETA VALUES, 843
Alexandru Popa (2014)
On the trace formula for Hecke operators on congruence subgroups, IIResearch in the Mathematical Sciences, 5
J-P Serre (1997)
Répartition asymptotique des valeurs propres de l’opérateur de Hecke $$T_p$$ T pJ. AMS, 10
G Shimura (1974)
10.1007/BF02392117Acta Math., 132
(1974)
Explicit formula of the traces of Hecke operators for 0(N)
G Shimura (1974)
On the trace formula for Hecke operatorsActa Math., 132
S. Ahlgren (2002)
The Points of a Certain Fivefold over Finite Fields and the Twelfth Power of the Eta FunctionFinite Fields and Their Applications, 8
A. Selberg (1956)
Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet seriesJournal of the Indian Mathematical Society, 20
(1976)
Séminaire de Théorie des Nombres de Bordeau
In a previous paper, we obtained a general trace formula for double coset operators acting on modular forms for congruence subgroups, expressed as a sum over conjugacy classes. Here we specialize it to the congruence subgroups $$\Gamma _0(N)$$ Γ 0 ( N ) and $$\Gamma _1(N)$$ Γ 1 ( N ) , obtaining explicit formulas in terms of class numbers for the trace of a composition of Hecke and Atkin–Lehner operators. The formulas are among the simplest in the literature and hold without any restriction on the index of the operators. We give two applications of the trace formula for $$\Gamma _1(N)$$ Γ 1 ( N ) : we determine explicit trace cusp forms for $$\Gamma _0(4)$$ Γ 0 ( 4 ) with Nebentypus, and we compute the limit of the trace of a fixed Hecke operator as the level N tends to infinity.
Research in the Mathematical Sciences – Springer Journals
Published: Jan 22, 2018
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