Mean values and moments of arithmetic functions over number fields

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Arithmetic Height Functions over Finitely Generated Fields

In this paper, we propose a new height function for a variety defined over a finitely generated field overQ. For this height function, we will prove Northcott’s theorem and Bogomolov’s conjecture, so that we can recover the original Raynaud’s theorem (Manin-Mumford’s conjecture). CONTENTS Introduction 1 1. Arakelov intersection theory 3 2. Arithmetically positive hermitian line bundles 6 3. Ari...

متن کامل

Sums of Arithmetic Functions over Values of Binary Forms

Given a suitable arithmetic function h : N → R>0, and a binary form F ∈ Z[x1, x2], we investigate the average order of h as it ranges over the values taken by F . A general upper bound is obtained for this quantity, in which the dependence upon the coefficients of F is made completely explicit.

متن کامل

Jacobi Theta Functions over Number Fields

We use Jacobi theta functions to construct examples of Jacobi forms over number fields. We determine the behavior under modular transformations by regarding certain coefficients of the Jacobi theta functions as specializations of symplectic theta functions. In addition, we show how sums of those Jacobi theta functions appear as a single coefficient of a symplectic theta function. 2000 Mathemati...

متن کامل

Central Values of Hecke L-functions of Cm Number Fields

0. Introduction. It is well known that the zeta function of CM (complex multiplication) abelian varieties can be given in terms of L-functions of associated Hecke characters. In this paper, we prove a formula expressing the central special value of the L-function of certain Hecke characters in terms of theta functions. The formula easily implies that the central value is nonnegative and yields ...

متن کامل

Arithmetic over Function Fields

These notes accompany lectures presented at the Clay Mathematics Institute 2006 Summer School on Arithmetic Geometry. The lectures summarize some recent progress on existence of rational points of projective varieties defined over a function field over an algebraically closed field.

متن کامل

ذخیره 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: Research in Number Theory

سال: 2019

ISSN: 2522-0160,2363-9555

DOI: 10.1007/s40993-019-0160-3