Automorphic forms

Xem 1-8 trên 8 kết quả Automorphic forms
  • The present book collects most of the courses and seminars delivered at the meeting entitled “ Frontiers in Number Theory, Physics and Geometry”, which took place at the Centre de Physique des Houches in the French Alps, March 9- 21, 2003. It is divided into two volumes. Volume I contains the contributions on three broad topics: Random matrices, Zeta functions and Dynamical systems. The present volume contains sixteen contributions on three themes: Conformal field theories for strings and branes, Discrete groups and automorphic forms and finally, Hopf algebras and renormalization....

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  • Introduction In 1903 Voronoi [42] postulated the existence of explicit formulas for sums of the form (1.1) n≥1 an f (n) , for any “arithmetically interesting” sequence of coefficients (an )n≥1 and every f in a large class of test functions, including characteristic functions of bounded intervals. He actually established such a formula when an = d(n) is the number of positive divisors of n [43]. He also asserted a formula for (1.2) an = #{(a, b) ∈ Z2 | Q(a, b) = n} , where Q denotes a positive definite integral quadratic form [44]; ...

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  • This is a report on the recent proof of the fundamental lemma. The fundamental lemma and the related transfer conjecture were formulated by R. Langlands in the context of endoscopy theory in [26]. Important arithmetic applications follow from endoscopy theory, including the transfer of automorphic representations from classical groups to linear groups and the construction of Galois representations attached to automorphic forms via Shimura varieties.

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  • In this paper we solve the subconvexity problem for Rankin-Selberg L-functions L(f ⊗ g, s) where f and g are two cuspidal automorphic forms over Q, g being fixed and f having large level and nontrivial nebentypus. We use this subconvexity bound to prove an equidistribution property for incomplete orbits of Heegner points over definite Shimura curves. L(f, s),

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  • Combining sieve methods with automorphic form theory and techniques from -adic cohomology, we prove that the sign of Kloosterman sums Kl(1, 1; n) changes infinitely often as n ranges over the squarefree integers having all their prime factors larger than n1/23.9 . 1. Introduction Soient a, b et n trois entiers, avec n 1. On rappelle que la somme de Kloosterman Kl(a, b; n) est d´finie par la formule e ax + bx Kl(a, b; n) = exp 2πi . n x mod n (x,n)=1 (la notation x indique l’inverse de x modulo n). Rappelons que c’est un nombre r´el, qui,...

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  • The theory of automorphic functions in one complex variable was created during the second half of the nineteenth and the beginning of the twentieth centuries. Important contributions are due to such illustrious mathematicians as F. Klein, P. Koebe and H. Poincare. Two sources may be traced: the uniformization theory of algebraic functions, and certain topics in number theory. Automorphic functions with respect to groups with compact quotient space on the one hand and elliptic modular functions on the other are examples of these two aspects.

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  • We prove that the existence of an automorphism of finite order on a Q-variety X implies the existence of algebraic linear relations between the logarithm of certain periods of X and the logarithm of special values of the Γ-function. This implies that a slight variation of results by Anderson, Colmez and Gross on the periods of CM abelian varieties is valid for a larger class of CM motives. In particular, we prove a weak form of the period conjecture of Gross-Deligne [11, p. 205]1 .

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  • This is the second of two papers in which we prove the Tits alternative for Out(Fn ). Contents 1. Introduction and outline 2. Fn -trees 2.1. Real trees 2.2. Real Fn -trees 2.3. Very small trees 2.4. Spaces of real Fn -trees 2.5. Bounded cancellation constants 2.6. Real graphs 2.7. Models and normal forms for simplicial Fn -trees 2.8. Free factor systems 3. Unipotent polynomially growing outer automorphisms 3.1. Unipotent linear maps 3.2. Topological representatives 3.3. Relative train tracks and automorphisms of polynomial growth 3.4. Unipotent representatives and UPG automorphisms ...

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