Japan-Korea Joint Seminar on Number Theory and Related Topics 2014 Chida, Masataka Title: Regulators and special values of Rankin-Selberg L-functions Abstract: This is a joint work with Fran¸cois Brunault. In this talk,

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APPEARED IN BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY Volume 31, Number 1, July 1994, Pages 1-14 SELBERG’S CONJECTURES AND ARTIN L-FUNCTIONS

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• Algebra
• Abstract algebra
• Mathematics
• Conjectures
• Automorphic forms
• Class field theory
• Representation theory of Lie groups
• Algebraic number theory
• Artin L-function
• Selberg class
• Langlands program
• RamanujanPetersson conjecture

The Rankin-Selberg method for automorphic distributions Stephen D. Miller? and Wilfried Schmid?? 1 2

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• Mathematical analysis
• Mathematics
• Fourier analysis
• Modular forms
• Generalized functions
• Analytic number theory
• Special functions
• RankinSelberg method
• Maass wave form
• Fourier transform
• Bessel function
• Dirac delta function

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS Volume 15, Number 2, Spring 1985 ON THE ESTIMATION OF EIGENVALUES OF HECKE OPERATORS

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• Mathematical analysis
• Mathematics
• Modular forms
• Conjectures
• Analytic number theory
• Srinivasa Ramanujan
• RamanujanPetersson conjecture
• Mathematical series
• Hecke operator
• Dirichlet series
• Selberg class
• Fourier transform

Research Statement Brandon Fodden The central focus of my research is the study of L-functions. A combination of powerful results and fundamental open questions makes this an exciting area in which to do research. The st

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• Bernhard Riemann
• Analytic number theory
• Conjectures
• Field theory
• Algebraic geometry
• Generalized Riemann hypothesis
• Riemann zeta function
• Riemann hypothesis
• Prime number theorem
• Elliptic curve
• Diophantine equation
• Selberg class

709 Documenta Math. Special Values of Anticyclotomic Rankin-Selberg L-Functions

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• Field theory
• Number theory
• Distribution
• Hecke character
• Valuation
• P-adic L-function
• Iwasawa theory
• Building
• P-adic number
• Decomposition of spectrum
• Symbol

The Hardy-Ramanujan Asymptotic Partition Formula

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• Number theorists
• Srinivasa Ramanujan
• Fellows of the Royal Society
• Combinatorics
• Number theory
• Partition
• G. H. Hardy
• Atle Selberg
• George Andrews
• Ramanujan
• 1729
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PERlon FUNCTIONS AND THE SELBERG ZETA FUNCTION FOR TUE MODULAR GROUP John Lewis and Don Zagier Framingham State College

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• Analytic number theory
• Bernhard Riemann
• Automorphic forms
• Selberg trace formula
• Selberg zeta function
• Riemann zeta function
• ArthurSelberg trace formula
• Riemann hypothesis

II. Int´egrales de Rankin-Selberg, facteurs L locaux et transformation de Fourier Rappelons qu’on part d’une fonction localement constante ψ W(r)

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Appendix by D. Zagier The Eichler-Selberg Trace Formula on SLiZ) Throughout this appendix we let r=r(1)=SL 2 (Z). We let Fbe a fundamental domain for r in D. We fix a weight k even ~4. We write T(m) instead of Tk(m) for

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• Mathematical analysis
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• Integral calculus
• Order of integration
• Moduli theory
• Singular integral operators of convolution type
• Oscillator representation