دانلود کتاب Theta Functions : From the Classical to the Modern

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Cover Title page Contents Preface Ramanujan's Theory of Theta-Functions, Bruce C. Berndt 1. Definitions 2. Ramanujan's ₁?₁ summation and the Jacobi triple product identity 3. Basic multiplicative and additiveproperties, including Schröter's formulas 4. Quintuple product identity 5. Applications to Lambert series and sums of squares 6. Elliptic integrals 7. Inversion formulas 8. Catalogue of theta-function evaluations 9. Modular equations 10. Eta-function identities 11. Theta-function identities and work of R. J. Evans 12. Ramanujan's Eisenstein series P, Q, and R 13. Ramanujan's theories of elliptic functions to alternative bases References Eisenstein Series and Theta Functions on the Metaplectic Group, Jeff Hoffstein Introduction 1. Eisenstein series and theta functions on the double cover of GL(2) 2. The n-fold cover of GL(2) 3. Eisenstein series and theta functions over function fields 4. Some GL(3) examples 5. Theta functions on the n-fold cover of GL(r) 6. The Group GSp(2n) References Weil Representation, Howe Duality, and the Theta Correspondence, Dipendra Prasad 1. Heisenberg group 2. Metaplectic group and the Weil representation 3. Dual reductive pairs 4. Howe duality 5. Howe conjecture in the Archimedean case 6. The spherical case 7. Seesaw pairs 8. The theta correspondence 9. Questions References On Theta-Series Liftings for Unitary Groups, Stephen Gelbart Introductory remarks 1. Weil's representation and theta-series 2. Howe's correspondence and theta-series liftings 3. Specialization to the unitary group U(3) 4. Trace formula results 5. L-functions for U(3) 6. Characterization of endoscopic representations Appendix. Explicit formulas for the Weil representation restricted to unipotent elements of U(V) X U(Φ') References Back Cover