On the Trace of Hecke Operators for Maass Forms for Congruence Subgroups II

J. Brian Conrey, Xian‐Jin Li

Type: Article

Publication Date: 2005-01-01

Citations: 10

DOI: https://doi.org/10.1515/form.2005.17.1.1

Abstract

Let Eλ be the Hilbert space spanned by the eigenfunctions of the non-Euclidean Laplacian associated with a positive discrete eigenvalue λ. In this paper, the trace of the Hecke operators acting on the space Eλ is computed explicitly for Hecke congruence subgroups of non-square free level.

Locations

arXiv (Cornell University) - View - PDF
Forum Mathematicum - View

Similar Works

Action	Title	Year	Authors
+	On the trace of Hecke operators for Maass forms for congruence subgroups II	2001	Xian‐Jin Li
+	On the trace of Hecke Operators for Maass forms for congruence subgroups	1999	J. Brian Conrey Xian‐Jin Li
+ PDF Chat	On the trace of Hecke operators for Maass forms for congruence subgroups	2001	J. Brian Conrey Xian‐Jin Li
+	Congruences for eigenvalues of hecke operators on SL2 (Z)	1981	Kazuyuki Hatada
+	On the trace of Hecke operators for Maass forms	1999	Xian‐Jin Li
+	New models for the action of Hecke operators in spaces of Maass wave forms	2007	Ian Kiming
+ PDF Chat	On the trace formula for Hecke operators on congruence subgroups, II	2018	Alexandru A. Popa
+	Congruences for Hecke eigenvalues in minus spaces	2020	Soyoung Choi Chang Heon Kim Kyung Seung Lee
+	Kloosterman sums for Clifford algebras and a lower bound for the positive eigenvalues of the Laplacian for congruence subgroups acting on hyperbolic spaces	1990	Jürgen Elstrodt Fritz Grunewald J. Mennicke
+	On the Hecke Eigenvalues of Maass Forms	2014	Wenzhi Luo Zhou Fan
+	Congruences for eigenvalues of Hecke operators on Siegel modular forms of degree two	1986	Shin-ichiro Mizumoto
+ PDF Chat	Eigenvalues of the Laplacian for Hecke triangle groups	1992	Dennis A. Hejhal
+	The determinant invariant for operators with trace class self commutators	1973	Lawrence G. Brown
+ PDF Chat	On Eigenvalues of the Laplacian for Hecke Triangle Groups	2018	Dennis A. Hejhal
+	Roots of quadratic congruences and eigenvalues of the non-Euclidean Laplacian	1986	Dennis A. Hejhal
+	The trace of Hecke operators	1968	F. I. Mautner
+	Congruences for Hecke eigenvalues in higher level cases	2011	Soyoung Choi Chang Heon Kim
+ PDF Chat	On the Hecke eigenvalues of Maass forms	2019	Wenzhi Luo Zhou Fan
+ PDF Chat	Maass wave forms, quantum modular forms and Hecke operators	2018	Seewoo Lee
+	Trace formulas and their applications on Hecke eigenvalues	2012	Yingnan Wang

Works That Cite This (9)

Action	Title	Year	Authors
+	On exceptional eigenvalues of the Laplacian for Γ₀(𝑁)	2008	Xian‐Jin Li
+	On exceptional eigenvalues of the Laplacian for $Γ_0(N)$	2006	Xian‐Jin Li
+ PDF Chat	The Selberg trace formula as a Dirichlet series	2016	Andrew R. Booker Min Lee
+	None	2001	Andreas Strömbergsson
+	The Selberg trace formula as a Dirichlet series	2015	Andrew R. Booker Min Lee
+	THE PRIME GEODESIC THEOREM AND QUANTUM MECHANICS ON FINITE VOLUME GRAPHS: A REVIEW	2001	Norman E. Hurt
+	Traces of Hecke operators acting on three-dimensional hyperbolic space	2006	Nicole Raulf
+	On the physical interpretation of the Riemann zeta function, the Rigid Surface Operators in Gauge Theory, the adeles and ideles groups applied to various formulae regarding the Riemann zeta function and the Selberg trace formula, p-adic strings, zeta strings and p-adic cosmology and mathematical connections with some sectors of String Theory and Number Theory.	2008	Michele Nardelli
+ PDF Chat	On the relative distribution of eigenvalues of exceptional Hecke operators and automorphic Laplacians	2006	Erik Balslev Alexei B. Venkov

Works Cited by This (21)

Action	Title	Year	Authors
+	Introduction to the spectral theory of automorphic forms	1995	Henryk Iwaniec
+ PDF Chat	Über die Classenzahl quadratischer Zahlkörper	1935	Carl Ludwig Siegel
+	Topics in Classical Automorphic Forms	1997	Henryk Iwaniec
+	Introduction to number theory	2009	Luo Hua
+ PDF Chat	The Selberg trace formula for modular correspondences	1990	Shigeki Akiyama Yoshio Tanigawa
+	Kloosterman sums and Fourier coefficients of cusp forms	1982	Jean-Marc Deshouillérs Henryk Iwaniec
+	The Selberg trace formula and the Riemann zeta function	1976	Dennis A. Hejhal
+	Heegner points and derivatives ofL-series. II	1987	Benedict H. Gross Winfried Kohnen Don Zagier
+	Class numbers of indefinite binary quadratic forms II	1985	Peter Sarnak
+	A Treatise on the Theory of Bessel Functions.	1923	Matthew Porter G. N. Watson