A Poisson Summation Formula for Extensions of Number Fields

2000 ◽  
Vol 61 (1) ◽  
pp. 36-50
Author(s):  
Eduardo Friedman ◽  
Nils-Peter Skoruppa
Keyword(s):  
Summation Formula ◽  
Number Fields ◽  
Poisson Summation Formula ◽  
Poisson Summation

scholarly journals A quadratic large sieve inequality over number fields

2012 ◽  
Vol 154 (2) ◽  
pp. 193-212 ◽  
Author(s):  
LEO GOLDMAKHER ◽  
BENOÎT LOUVEL
Keyword(s):  
Number Field ◽  
Summation Formula ◽  
Number Fields ◽  
Poisson Summation Formula ◽  
Basic Theory ◽  
Large Sieve ◽  
Large Sieve Inequality ◽  
Poisson Summation

AbstractWe formulate and prove a large sieve inequality for quadratic characters over a number field. To do this, we introduce the notion of an n-th order Hecke family. We develop the basic theory of these Hecke families, including versions of the Poisson summation formula.

scholarly journals Computing dimensions of spaces of Arakelov divisors of number fields

2017 ◽  
Vol 13 (02) ◽  
pp. 487-512
Author(s):  
Ha Thanh Nguyen Tran
Keyword(s):  
Number Field ◽  
Algebraic Curve ◽  
Summation Formula ◽  
Unit Group ◽  
Number Fields ◽  
Poisson Summation Formula ◽  
Jump Algorithm ◽  
Poisson Summation

The function [Formula: see text] for a number field is analogous to the dimension of the Riemann–Roch spaces at divisors on an algebraic curve. We provide a method to compute this function for number fields with unit group of rank at most 2, even with large discriminant. This method is based on using LLL-reduced bases, the “jump algorithm” and Poisson summation formula.

scholarly journals Some Finite Analogues of the Poisson Summation Formula

1961 ◽  
Vol 12 (3) ◽  
pp. 133-138 ◽  
Author(s):  
L. Carlitz
Keyword(s):  
Summation Formula ◽  
Poisson Summation Formula ◽  
Euler’S Constant ◽  
Image Position ◽  
Positive Integers ◽  
Euler's Constant ◽  
Poisson Summation

1. Guinand (2) has obtained finite identities of the typewhere m, n, N are positive integers and eitherorwhere γ is Euler's constant and the notation ∑′ indicates that when x is integral the term r = x is multiplied by ½. Clearly there is no loss of generality in taking N = 1 in (1.1).

scholarly journals A strong version of Poisson summation

1997 ◽  
Vol 20 (1) ◽  
pp. 81-92 ◽  
Author(s):  
Nelson Petulante
Keyword(s):  
Summation Formula ◽  
Poisson Summation Formula ◽  
Strong Version ◽  
Poisson Summation

We establish a generalized version of the classical Poisson summation formula. This formula incorporates a special feature called “compression”, whereby, at the same time that the formula equates a series to its Fourier dual, the compressive feature serves to enable both sides of the equation to converge.

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