**Proceedings of Symposia in Pure Mathematics**

Volume: 75;
2006;
303 pp;
Hardcover

MSC: Primary 11;
Secondary 22

Print ISBN: 978-0-8218-3963-8

Product Code: PSPUM/75

List Price: $75.00

Individual Member Price: $60.00

**Electronic ISBN: 978-0-8218-9381-4
Product Code: PSPUM/75.E**

List Price: $75.00

Individual Member Price: $60.00

# Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory

Share this page *Edited by *
*Solomon Friedberg; Daniel Bump; Dorian Goldfeld; Jeffrey Hoffstein*

Multiple Dirichlet series are Dirichlet series in several complex variables. A multiple Dirichlet series is said to be perfect if it satisfies a finite group of functional equations and has meromorphic continuation everywhere. The earliest examples came from Mellin transforms of metaplectic Eisenstein series and have been intensively studied over the last twenty years. More recently, many other examples have been discovered and it appears that all the classical theorems on moments of \(L\)-functions as well as the conjectures (such as those predicted by random matrix theory) can now be obtained via the theory of multiple Dirichlet series. Furthermore, new results, not obtainable by other methods, are just coming to light. This volume offers an account of some of the major research to date and the opportunities for the future. It includes an exposition of the main results in the theory of multiple Dirichlet series, and papers on moments of zeta- and \(L\)-functions, on new examples of multiple Dirichlet series, and on developments in the allied fields of automorphic forms and analytic number theory.

#### Table of Contents

# Table of Contents

## Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory

- Contents vii8 free
- Preface ix10 free
- List of Participants xi12 free
- Multiple Dirichlet Series and Their Applications 114 free
- Multiple Dirichlet series and automorphic forms 316
- Applications of multiple Dirichlet series in mean values of L-functions 4356
- Second moments of quadratic Hecke L-series and multiple Dirichlet series I 5972
- Weyl group multiple Dirichlet series I 91104
- Residues of Weyl group multiple Dirichlet series associated to GL[sub(n+1)] 115128
- Multiple Hurwitz zeta functions 135148
- Multiple zeta values over global function fields 157170
- Generalised Selberg zeta functions and a conjectural Lefschetz formula 177190

- Automorphic Forms and Analytic Number Theory 191204
- Rankin-Cohen brackets on higher order modular forms 193206
- Eulerian integrals for GL[sub(n)] 203216
- Is the Hlawka zeta function a respectable object? 225238
- On sums of integrals of powers of the zeta-function in short intervals 231244
- Uniform bounds for Rankin-Selberg L-functions 243256
- Mean values of zeta-functions via representation theory 257270
- On the pair correlation of the eigenvalues of the hyperbolic Laplacian for PSL(2,Z)\H II 281294
- Lower bounds for moments of L-functions: Symplectic and orthogonal examples 293306

#### Readership

Graduate students and research mathematicians interested in number theory, especially automorphic forms and connections to analytic number theory.