Description
Book SynopsisWeyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. This book proves foundational results about these series and develops their combinatorics.
Table of Contents*FrontMatter, pg. i*Contents, pg. v*Preface, pg. vii*Chapter One. Type A Weyl Group Multiple Dirichlet Series, pg. 1*Chapter Two. Crystals and Gelfand-Tsetlin Patterns, pg. 10*Chapter Three. Duality, pg. 22*Chapter Four. Whittaker Functions, pg. 26*Chapter Five. Tokuyama's Theorem, pg. 31*Chapter Six. Outline of the Proof, pg. 36*Chapter Seven. Statement B Implies Statement A, pg. 51*Chapter Eight. Cartoons, pg. 54*Chapter Nine. Snakes, pg. 58*Chapter Ten. Noncritical Resonances, pg. 64*Chapter Eleven. Types, pg. 67*Chapter Twelve. Knowability, pg. 74*Chapter Thirteen. The Reduction to Statement D, pg. 77*Chapter Fourteen. Statement E Implies Statement D, pg. 87*Chapter Fifteen. Evaluation of LAMBDAGAMMA and LAMBDADELTA, and Statement G, pg. 89*Chapter Sixteen. Concurrence, pg. 96*Chapter Seventeen. Conclusion of the Proof, pg. 104*Chapter Eighteen. Statement B and Crystal Graphs, pg. 108*Chapter Nineteen. Statement B and the Yang-Baxter Equation, pg. 115*Chapter Twenty. Crystals and p-adic Integration, pg. 132*Bibliography, pg. 143*Notation, pg. 149*Index, pg. 155
