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Analytic continuation ofζ 3 (S,K) to the critical strip. Arithmetic part

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Abstract

In this paper we study the zeta-function

$$\zeta _3 (s,K) = \sum\limits_{n = 1}^\infty {\frac{{\tau _3 (n)\tau _3 (n + K)}}{{(\sqrt {n(n + K)} )^S }}}$$

with the help of the technique of automorphic functions for SL3(Z).

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Literature cited

  1. A. I. Vinogradov and L. A. Takhtadzhyan, “Theory of Eisenstein series for the group SL(З,ℤ) and its application to a binary problem,” J. Sov. Math.,18, No. 3 (1982).

  2. A. I. Vinogradov and L. A. Takhtadzhyan, “Zeta-function of an additive problem of divisors and spectral decomposition of the automorphic Laplacian,” J. Sov. Math.,36, No. 1 (1987).

  3. N. V. Kuznetsov, “Convolution of Fourier coefficients of Eisenstein-Maas series,” J. Sov. Math.,29, No. 2 (1985).

  4. N. V. Kuznetsov, “Petersson conjecture for parabolic forms of weight zero and Linnik's conjecture,” Mat. Sb.,111, No. 3, 333–384 (1980).

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Authors
  1. A. I. Vinogradov
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 162, pp. 43–76, 1987.

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Vinogradov, A.I. Analytic continuation ofζ 3 (S,K) to the critical strip. Arithmetic part. J Math Sci 46, 1734–1759 (1989). https://doi.org/10.1007/BF01099346

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  • DOI: https://doi.org/10.1007/BF01099346

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