Families of Cusp Forms
نویسنده
چکیده
1. Families of cusp forms and the local equidistribution problem 2 2. Families of L-functions 6 3. Analogy with sieve 8 4. Examples of local equidistribution 8 5. Families of cusp forms according to Sarnak’s letter 11 6. Families of L-functions according to Conrey, Farmer, Keating, Rubinstein and Snaith 13 7. Direct consequences of strong local equidistribution 14 8. Quantitative local equidistribution: level of decay 15 9. Symmetry types for the behavior of L-functions on the critical line 18 10. Symmetry types and moments of L-functions 24 11. Orthogonal symmetry types 27 12. Other examples of symmetry types 28 13. An example with Siegel modular forms 30 References 34
منابع مشابه
Ramanujan - type results for Siegel cusp forms of degree 2
A result of Chai–Faltings on Satake parameters of Siegel cusp forms together with the classification of unitary, unramified, irreducible, admissible representations of GSp4 over a p-adic field, imply that the local components of the automorphic representation of GSp4 attached to a cuspidal Siegel eigenform of degree 2 must lie in certain families. Applications include estimates on Hecke eigenva...
متن کاملp-adic Banach modules of arithmetical modular forms and triple products of Coleman's families
For a prime number p ≥ 5, we consider three classical cusp eigenforms
متن کاملElliptic Curves , Modular Forms and Related
Nick Andersen (University of California, Los Angeles) Kloosterman sums and Maass cusp forms of half-integral weight ABSTRACT: Kloosterman sums play an important role in modern analytic number theory. I will give a brief survey of what is known about the classical Kloosterman sums and their connection to Maass cusp forms of weight 0. I will then talk about recent progress toward bounding sums of...
متن کاملColeman Power Series for K 2 and p - Adic Zeta Functions of Modular Forms dedicated to Professor
For a usual local field of mixed characteristic (0, p), we have the theory of Coleman power series [Co]. By applying this theory to the norm compatible system of cyclotomic elements, we obtain the p-adic Riemann zeta function of Kubota-Leopoldt [KL]. This application is very important in cyclotomic Iwasawa theory. In [Fu1], the author defined and studied Coleman power series for K2 for certain ...
متن کاملUniform behavior of families of Galois representations on Siegel modular forms
We prove the following uniformity principle: if one of the Galois representations in the family attached to a genus two Siegel cusp form of level 1, weight k > 3 and with multiplicity one is reducible (for a prime p > 4k − 5) then almost all the representations in the family are reducible. The result will be proved more generally for compatible families of geometric, pure and symplectic four-di...
متن کامل