Errata to “Average Values of Modular L-series Via the Relative Trace Formula”
نویسندگان
چکیده
منابع مشابه
A Trace Formula of Special Values of Automorphic L-functions
Deligne introduced the concept of special values of automorphic L-functions. The arithmetic properties of these L-functions play a fundamental role in modern number theory. In this paper we prove a trace formula which relates special values of the Hecke, Rankin, and the central value of the Garrett triple L-function attached to primitive newforms. This type of trace formula is new and involves ...
متن کاملAverage Distributions and Product of Special Values of L-Series
Let E be an elliptic curve defined over the rationals. For any prime p of good reduction, let Ep be the elliptic curve over Fp obtained by reducing E mod p. Let ap(E) be the trace of the Frobenius morphism of Ep. Then, Hasse proved that #E(Fp) = p + 1 − ap(E) with |ap(E)| ≤ 2 √ p. The case ap(E) = 0 corresponds to supersingular reduction mod p. Let N be a positive integer. For a fixed r ∈ Z, an...
متن کاملEisenstein Series and the Trace Formula
In the first part of these notes we shall try to describe the main ideas in the theory. Let G be a reductive algebraic matrix group over Q. Then G(A) is the restricted direct product over all valuations v of the groups G(Qu). If v is finite, define Ku to be G(uJ if this latter group is a special maximal compact subgroup of G(Qu). This takes care of almost all v. For the remaining finite v, we l...
متن کاملHarmonic analysis for relative trace formula
Many questions on special values of L-functions are tied to the study of period integrals of automorphic forms. A notable example is the formula of Waldspurger ([22]) that relates the toric period on GL2 or its inner form to some central critical L-value. The conjecture of Gan, Gross and Prasad ([4]) started with the Gross-Prasad conjecture ([5]), as well as the refinement of Ichino and Ikeda (...
متن کاملEisenstein Series and the Selberg Trace Formula. Ii
The integral of the kernel of the trace formula against an Eisenstein series is investigated. The analytic properties of this integral imply the divisibility of the convolution L-function attached to a form by the zeta function of the field. Introduction. This paper is a sequel and generalization of [12], but can be read independently of that paper; in particular, we will repeat the description...
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: Pure and Applied Mathematics Quarterly
سال: 2009
ISSN: 1558-8599,1558-8602
DOI: 10.4310/pamq.2009.v5.n4.a10