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基本説明
Brings together a distinguished group of experts to explore automorphic forms, principally via the associated L-functions, representation theory, and geometry.
Full Description
In Contributions to Automorphic Forms, Geometry, and Number Theory, Haruzo Hida, Dinakar Ramakrishnan, and Freydoon Shahidi bring together a distinguished group of experts to explore automorphic forms, principally via the associated L-functions, representation theory, and geometry. Because these themes are at the cutting edge of a central area of modern mathematics, and are related to the philosophical base of Wiles' proof of Fermat's last theorem, this book will be of interest to working mathematicians and students alike. Never previously published, the contributions to this volume expose the reader to a host of difficult and thought-provoking problems. Each of the extraordinary and noteworthy mathematicians in this volume makes a unique contribution to a field that is currently seeing explosive growth. New and powerful results are being proved, radically and continually changing the field's make up. Contributions to Automorphic Forms, Geometry, and Number Theory will likely lead to vital interaction among researchers and also help prepare students and other young mathematicians to enter this exciting area of pure mathematics. Contributors: Jeffrey Adams, Jeffrey D.
Adler, James Arthur, Don Blasius, Siegfried Boecherer, Daniel Bump, William Casselmann, Laurent Clozel, James Cogdell, Laurence Corwin, Solomon Friedberg, Masaaki Furusawa, Benedict Gross, Thomas Hales, Joseph Harris, Michael Harris, Jeffrey Hoffstein, Herve Jacquet, Dihua Jiang, Nicholas Katz, Henry Kim, Victor Kreiman, Stephen Kudla, Philip Kutzko, V. Lakshmibai, Robert Langlands, Erez Lapid, Ilya Piatetski-Shapiro, Dipendra Prasad, Stephen Rallis, Dinakar Ramakrishnan, Paul Sally, Freydoon Shahidi, Peter Sarnak, Rainer Schulze-Pillot, Joseph Shalika, David Soudry, Ramin Takloo-Bigash, Yuri Tschinkel, Emmanuel Ullmo, Marie-France Vigneras, Jean-Loup Waldspurger.
Contents
Preface
Joe Shalika and the Fine Hall Days, 1968-1971
Chapter 1. Representation of the Two By Two Unimodular Group Over Local Fields
Chapter 2. Theta-10
Chapter 3. Discrete Series Characters of Division Algebras and GLn Over A P-adic Field
Chapter 4. Automorphic Representations of GSp(4)
Chapter 5. Elliptic Curves, Hilbert Modular Forms, And the Hodge Conjecture
Chapter 6. On the Global Gross-Prasad Conjecture For Yoshida Liftings
Chapter 7. Sums of Twisted GL(3) Automorphic L-Functions
Chapter 8. Harmonic Analysis of the Schwartz Space of \SL2(R)
Chapter 9. Equidistribution Des Points De Hecke
Chapter 10. Remarks On Rankin-Selberg Convolutions
Chapter 11. On Some Geometric Constructions Related to Theta Characteristics
Chapter 12. Can P-adic Integrals Be Computed?
Chapter 13. Occult Period Invariants And Critical Values of the Degree Four L-Function of GSp(4)
Chapter 14. On a Conjecture of Jacquet
Chapter 15. Integral Representation of Whittaker Functions
Chapter 16. A Spectral Identity For Skew Symmetric Matrices
Chapter 17. Generic Representations And Local Langlands Reciprocity Law For P-adic SO2n+1
Chapter 18. Larsen's Alternative, Moments, and the Monodromy of Lefschetz Pencils
Chapter 19. On the Holomorphy of Certain L-Functions
Chapter 20. Richardson Varieties in the Grassmannian
Chapter 21. Types and Covers for SL(2)
Chapter 22. Beyond Endoscopy
Chapter 23. An Analogue of a Conjecture of Mazur: A Question in Diophantine Approximation on Tori
Chapter 24. Existence of Ramanujan Primes for GL(3)
Chapter 25. Nonvanishing of L-Functions on R(S)=1
Chapter 26. Rational Points and Automorphic Forms
Chapter 27. Height Zeta Functions of Equivariant Compactifications of the Heisenberg Group
Chapter 28. On Highest Whittaker Models and Integral Structures
Chapter 29. Représentations de Réduction Unipotente Pour SO(2n+1): Quelques Conséquences D'un Article De Lusztig
