Journal of Soviet Mathematics

, Volume 52, Issue 3, pp 3056–3063

Arithmetic of quaternions and Eisenstein series

  • V. A. Gritsenko


In the paper one computes the Fourier coefficients of the Eisenstein series of the orthogonal group of signature (1, 4). The formulas show that the restriction of the Eisenstein series to the “imaginary” axis is a Dirichlet series, whose coefficients are the products of the L-series by the number of the representations of the given number as a sum of three squares.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    B. A. Venkov, Selected Works. Studies in Number Theory [in Russian], Nauka, Leningrad (1981).Google Scholar
  2. 2.
    A. B. Venkov, “The spectral theory of automorphic functions”, Trudy Mat. Inst. Akad. Nauk SSSR,153, 1–171 (1981).MathSciNetGoogle Scholar
  3. 3.
    V. A. Gritsenko, “The zeta function of degree six for Hermitian modular forms of genus 2”, Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,154, 46–66 (1986).MATHGoogle Scholar
  4. 4.
    Yu. V. Linnik, “Quaternions and Cayley numbers; some applications of the arithmetic of quaternions”, Usp. Mat. Nauk,4, No. 5, 49–98 (1949).MATHMathSciNetGoogle Scholar
  5. 5.
    G. Shimura, “On the holomorphy of certain Dirichlet series”, Proc. London Math. Soc. Ser. 3,31, No. 1, 79–98 (1975).MATHMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • V. A. Gritsenko

There are no affiliations available

Personalised recommendations