Modular symbols for reductive groups and p-adic Rankin–Selberg convolutions over number fields
نویسندگان
چکیده
منابع مشابه
MODULAR SYMBOLS FOR REDUCTIVE GROUPS AND p-ADIC RANKIN-SELBERG CONVOLUTIONS OVER NUMBER FIELDS
We give a construction of a wide class of modular symbols attached to reductive groups. As an application we construct a p-adic distribution interpolating the special values of the twisted Rankin-Selberg L-function attached to cuspidal automorphic representations π and σ of GLn and GLn−1 over a number field k. If π and σ are ordinary at p, our distribution is bounded and gives rise to a p-adic ...
متن کاملReductive Groups over Fields
These are lecture notes that Tony Feng live-TEXed from a course given by Brian Conrad at Stanford in“winter” 2015, which Feng and Conrad edited afterwards. Two substitute lectures were delivered (by Akshay Venkatesh and Zhiwei Yun) when Conrad was out of town. This is a sequel to a previous course on the general structure of linear algebraic groups; some loose ends from that course (e.g., Cheva...
متن کاملSMOOTH REPRESENTATIONS OF p-ADIC REDUCTIVE GROUPS
Smooth representations of p-adic groups arise in number theory mainly through the study of automorphic representations, and thus in the end, for example, from modular forms. We saw in the first lecture by Matt Emerton that a modular form, thought of as function on the set of lattices with level N structure, we obtain a function in C(GL2(Z)\GL2(R) × GL2(Z/N),C) satisfying certain differential eq...
متن کاملSUPERCUSPIDAL CHARACTERS OF REDUCTIVE p-ADIC GROUPS
We compute the characters of many supercuspidal representations of reductive p-adic groups. Specifically, we deal with representations that arise via Yu’s construction from data satisfying a certain compactness condition. Each character is expressed in terms of a depth-zero character of a smaller group, the (linear) characters appearing in Yu’s construction, Fourier transforms of orbital integr...
متن کاملHILBERT’S TENTH PROBLEM FOR FUNCTION FIELDS OF VARIETIES OVER NUMBER FIELDS AND p-ADIC FIELDS
Let k be a subfield of a p-adic field of odd residue characteristic, and let L be the function field of a variety of dimension n ≥ 1 over k. Then Hilbert’s Tenth Problem for L is undecidable. In particular, Hilbert’s Tenth Problem for function fields of varieties over number fields of dimension ≥ 1 is undecidable.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2011
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crelle.2011.018