Mathematical Notes

, Volume 73, Issue 1–2, pp 97–102 | Cite as

A Discrete Analog of the Poisson Summation Formula

  • A. V. Ustinov


The first part of this paper is concerned with the proof of a discrete analog of the Poisson summation formula. In the second part, we describe an elementary proof of a functional equation for the function \(\theta (t)\), based on the summation formula derived in the paper.

Poisson summation formula Gauss sum uniform grid Fourier series 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    N. Koblits, Introduction to Elliptic Curves and Modular Forms [in Russian], IO NMFI, Novokuznetsk, 2000.Google Scholar
  2. 2.
    A. A. Karatsuba, Foundations of the Analytic Theory of Numbers [in Russian], Nauka, Moscow, 1983.Google Scholar
  3. 3.
    G. I. Arkhipov, V. A. Sadovnichii, and V. N. Chubarikov, Lectures on the Calculus [in Russian], Vysshaya Shkola, Moscow, 1999.Google Scholar
  4. 4.
    E. Titchmarsh, Introduction to the Theory of Fourier Integrals, Second edition, Oxford Univ. Press, Oxford, 1948.Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • A. V. Ustinov
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityRussia

Personalised recommendations