The heat kernel, theta inversion and zetas on Г∖ G ∕ K

[1]  S. Lang,et al.  A gaussian space of test functions , 2005 .

[2]  S. Gelbart,et al.  Riemann's zeta function and beyond , 2003, math/0309478.

[3]  P. Sarnak Spectra of hyperbolic surfaces , 2003 .

[4]  E. Frenkel Recent advances in the Langlands Program , 2003, math/0303074.

[5]  S. Lang,et al.  Hilbert-Asai Eisenstein series, regularized products, and heat kernels , 1999, Nagoya Mathematical Journal.

[6]  J. Dodziuk,et al.  Spectral Asymptotics on Degenerating Hyperbolic 3-Manifolds , 1998 .

[7]  J. Jorgenson,et al.  A regularized heat trace for hyperbolic Riemann surfaces of finite volume , 1997 .

[8]  J. Jorgenson,et al.  Convergence of the Normalized Spectral Counting Function on Degenerating Hyperbolic Riemann Surfaces of Finite Volume , 1997 .

[9]  S. Lang,et al.  Extension of analytic number theory and the theory of regularized harmonic series from Dirichlet series to Bessel series , 1996 .

[10]  J. Jorgenson,et al.  CONVERGENCE OF THE HEAT KERNEL AND THE RESOLVENT KERNEL ON DEGENERATING HYPERBOLIC RIEMANN SURFACES OF FINITE VOLUME , 1995 .

[11]  A. Beardon The Geometry of Discrete Groups , 1995 .

[12]  Jay Jorgenson,et al.  Explicit Formulas for Regularized Products and Series , 1994 .

[13]  U. Bunke,et al.  The wave kernel for the Laplacian on the classical locally symmetric spaces of rank one, theta functions, trace formulas and the Selberg zeta function , 1994 .

[14]  Jay Jorgenson,et al.  Basic Analysis of Regularized Series and Products , 1993 .

[15]  S. Lang,et al.  On Cramér's theorem for general Euler products with functional equation , 1993 .

[16]  T. Willmore AN INTRODUCTION TO DIFFERENTIABLE MANIFOLDS AND RIEMANNIAN GEOMETRY (Second edition) , 1987 .

[17]  F. Grunewald,et al.  Zeta-functions of binary Hermitian forms and special values of Eisenstein series on three-dimensional hyperbolic space , 1987 .

[18]  D. R. Heath-Brown,et al.  The Theory of the Riemann Zeta-Function , 1987 .

[19]  P. Sarnak,et al.  The determinant of the Eisenstein matrix and Hilbert class fields , 1985 .

[20]  Peter Sarnak,et al.  The arithmetic and geometry of some hyperbolic three manifolds , 1983 .

[21]  H. Moscovici,et al.  L2-index and the Selberg trace formula , 1983 .

[22]  M. Atiyah,et al.  Eta invariants, signature defects of cusps, and values of L-functions , 1983 .

[23]  A. Borel,et al.  LAPLACIAN AND THE DISCRETE SPECTRUM OF AN ARITHMETIC GROUP , 1983 .

[24]  P. Zograf Selberg trace formula for the Hilbert modular group of a real quadratic algebraic number field , 1982 .

[25]  Henryk Iwaniec,et al.  Kloosterman sums and Fourier coefficients of cusp forms , 1982 .

[26]  Zagier Don The Rankin-Selberg method for automorphic functions which are not of rapid decay , 1982 .

[27]  R. Gangolli,et al.  Zeta functions of Selberg’s type for some noncompact quotients of symmetric spaces of rank one , 1980, Nagoya Mathematical Journal.

[28]  J. Arthur A trace formula for reductive groups I terms associated to classes in $G(\mathbf{Q})$ , 1978 .

[29]  Mogens Flensted-Jensen,et al.  Spherical functions on a real semisimple Lie group. A method of reduction to the complex case , 1978 .

[30]  R. Gangolli Zeta functions of Selberg's type for compact space forms of symmetric spaces of rank one , 1977 .

[31]  R. Langlands On the Functional Equations Satisfied by Eisenstein Series , 1976 .

[32]  J. Arthur The Selberg Trace Formula for Groups of F-rank One , 1974 .

[33]  V. K. Patodi,et al.  On the heat equation and the index theorem , 1973 .

[34]  H. P. McKean,et al.  Selberg's trace formula as applied to a compact riemann surface , 1972 .

[35]  P. Griffiths Complex-Analytic Properties of Certain Zariski Open Sets on Algebraic Varieties , 1971 .

[36]  T. Asai On a Certain Function Analogous to log|η(z)| , 1970, Nagoya Mathematical Journal.

[37]  W. Geyer Unendliche algebraische Zahlkörper, über denen jede Gleichung auflösbar von beschränkter Stufe ist , 1969 .

[38]  Harish-Chandra,et al.  Automorphic Forms on Semisimple Lie Groups , 1968 .

[39]  R. Gangolli Asymptotic behaviour of spectra of compact quotients of certain symmetric spaces , 1968 .

[40]  Tomio Kubota Über Diskontinuierliche Gruppen Picardschen Typus und Zugehörige Eisensteinsche Reihen , 1968, Nagoya Mathematical Journal.

[41]  W. Roelcke Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. II , 1966 .

[42]  Harish-Chandra Invariant eigendistributions on a semisimple lie algebra , 1965 .

[43]  S. Lang Introduction to Differentiable Manifolds , 1964 .

[44]  S. Helgason,et al.  Differential operators on homogeneous spaces , 1959 .

[45]  T. Ono On Some Arithmetic Properties of Linear Algebraic Groups , 1959 .

[46]  M. P. Gaffney The conservation property of the heat equation on riemannian manifolds , 1959 .

[47]  Harish-Chandra Spherical functions on a semi-simple Lie group I , 1958 .

[48]  H. Maass Über eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichlet scher Reihen durch Funktionalgleichungen , 1949 .

[49]  H. Cramér Studien über die Nullstellen der Riemannschen Zetafunktion , 1919 .

[50]  S. Lang,et al.  Heat Eisenstein series on _ , 2009 .

[51]  Jay Jorgenson,et al.  The Ubiquitous Heat Kernel , 2006 .

[52]  S. Lang,et al.  Collected Papers Volume III , 2000 .

[53]  S. Lang,et al.  Math Talks for Undergraduates , 1999 .

[54]  Fritz Grunewald,et al.  Groups Acting on Hyperbolic Space , 1998 .

[55]  H. Iwaniec Introduction to the spectral theory of automorphic forms , 1995 .

[56]  G. Rota Harmonic analysis of spherical functions on real reductive groups: R. Gangolli and V. S. Varadarajan, Springer, 1988, 365 pp. , 1990 .

[57]  J. Arthur The Trace Formula and Hecke Operators , 1989 .

[58]  V. Varadarajan,et al.  The Elementary Spherical Functions , 1988 .

[59]  I. Efrat The Selberg trace formula for ₂()ⁿ , 1987 .

[60]  M. Flensted-jensen Analysis on non-Riemannian symmetric spaces , 1986 .

[61]  S. Helgason Groups and geometric analysis , 1984 .

[62]  W. Müller Signature defects of cusps of Hilbert modular varieties and values of $L$-series at $s=1$ , 1984 .

[63]  W. Müller Spectral Theory for Riemannian Manifolds with Cusps and a Related Trace Formula , 1983 .

[64]  A. J. Poorten,et al.  Multiplicative dependence in number-fields , 1983 .

[65]  S. Lang Real and Functional Analysis , 1983 .

[66]  D. Hejhal The Selberg trace formula for PSL (2, IR) , 1983 .

[67]  J. Dodziuk,et al.  Maximum principle for parabolic inequalities and the heat flow on open manifolds , 1983 .

[68]  J. Szmidt The Selberg trace formula for the Picard group SL(2, Z[i]) , 1983 .

[69]  J. Arthur A trace formula for reductive groups II: applications of a truncation operator , 1980 .

[70]  富雄 久保田 Elementary theory of Eisenstein series , 1973 .

[71]  S. Lang Algebraic Number Theory , 1971 .

[72]  A. Borel,et al.  Introduction aux groupes arithmétiques , 1969 .

[73]  K. Hirsch,et al.  Representation theory and automorphic functions , 1969 .

[74]  L. Gårding Vecteurs analytiques dans les représentations des groupes de Lie , 1960 .

[75]  W. Roelcke Über die Wellengleichung bei Grenzkreisgruppen erster Art , 1956 .

[76]  Harish-Chandra Representations of semisimple Lie groups. II , 1954 .

[77]  É. Picard Sur un groupe de transformations des Points de l'espace situés du même côté d'un plan , 1884 .