Poisson Summation on Regular Regions

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).

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Weil type representations and automorphic forms

Nagoya Mathematical Journal ◽

10.1017/s0027763000018730 ◽

1980 ◽

Vol 77 ◽

pp. 145-166 ◽

Cited By ~ 3

Author(s):

Toshiaki Suzuki

Keyword(s):

Dirichlet Series ◽

Functional Equations ◽

Theta Series ◽

Type Representation ◽

Generalized Poisson ◽

Summation Formulae ◽

Reciprocity Law ◽

Weil Type ◽

Generalized Theta Series ◽

Poisson Summation

During 1934-1936, W. L. Ferrar investigated the relation between summation formulae and Dirichlet series with functional equations, inspired by Voronoi’s works (1904) on summation formula with respect to the numbers of divisors. In [11] A. Weil showed that the automorphic properties of theta series are expressed by generalized Poisson summation formulae with respect to the so-called Weil representation. On the other hand, T. Kubota, in his study of the reciprocity law in a number field, defined a generalized theta series and a generalized Weil type representation of SL(2, C) and obtained similar results to those of A. Weil (1970-1976, [5], [6], [7]). The methods, used by W. L. Ferrar and T. Kubota, to obtain (generalized Poisson) summation formulae depend similarly on functional equations of Dirichlet series (attached to the generalized theta series).

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Some generalisations of the Poisson summation formula

Journal of Physics A General Physics ◽

10.1088/0305-4470/13/5/549 ◽

1980 ◽

Vol 13 (5) ◽

pp. 1901-1901

Author(s):

B J B Crowley

Keyword(s):

Summation Formula ◽

Poisson Summation Formula ◽

Poisson Summation

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Theoretical solutions for degree distribution of decreasing random birth-and-death networks

Modern Physics Letters B ◽

10.1142/s0217984917501615 ◽

2017 ◽

Vol 31 (14) ◽

pp. 1750161 ◽

Cited By ~ 1

Author(s):

Yin Long ◽

Xiao-Jun Zhang ◽

Kui Wang

Keyword(s):

Steady State ◽

Computer Simulations ◽

Generating Function ◽

Degree Distribution ◽

Probability Generating Function ◽

Function Approach ◽

Poisson Summation

In this paper, theoretical solutions for degree distribution of decreasing random birth-and-death networks [Formula: see text] are provided. First, we prove that the degree distribution has the form of Poisson summation, for which degree distribution equations under steady state and probability generating function approach are employed. Then, based on the form of Poisson summation, we further confirm the tail characteristic of degree distribution is Poisson tail. Finally, simulations are carried out to verify these results by comparing the theoretical solutions with computer simulations.

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