Journal of Mathematical Sciences

, Volume 137, Issue 2, pp 4617–4633 | Cite as

A generalized square of the zeta function. Spectral decompositions

  • A. I. Vinogradov


The spectral decomposition for the square of the classical Riemann zeta function ζ2(s) is generalized to the case of the product of two such functions ζ(s1) · ζ(s2) of different arguments. Bibliography: 6 titles.


Functional Equation Spectral Function Zeta Function Spectral Decomposition Dirichlet Series 
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  1. 1.
    A. I. Vinogradov, (a) “Points beneath a hyperbola. A spectral approach,” Zap. Nauchn. Semin. POMI, 289, 63–76. (2002). (b) “Binary problems. A spectral approach. II, III,” Zap. Nauchn. Semin. POMI, 251, 178–194, 195–215 (1998).MATHGoogle Scholar
  2. 2.
    E. C. Titchmarsh, The Theory of the Riemann Zeta Function, Oxford (1951).Google Scholar
  3. 3.
    R. Kaufman, “On A. F. Lavrik’s shortened equation,” Zap. Nauchn. Semin. POMI, 76, 124–159 (1978).MATHMathSciNetGoogle Scholar
  4. 4.
    V. Bykovsky, N. Kuznetsov, and A. Vinogradov, “Generalized summation formula for an inhomogenious convolution,” in: International Conference on Automorphic Functions and Their Applications, Khabarovsk (1988), pp. 18–64.Google Scholar
  5. 5.
    H. Bateman and A. Erdelyi, Higher Trancendental Functions, Vol. 2 (1953).Google Scholar
  6. 6.
    N. V. Kuznetsov, “The Peterson conjecture for parabolic forms of weight zero and the Linnik conjecture. I. A sum of Kloostermann sums,” Mat. Sb., 3, No. 3, 334–383 (1980).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. I. Vinogradov
    • 1
  1. 1.St.Petersburg Department of the Steklov Mathematical InstituteSt.PetersburgRussia

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