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Summation of the euler function values over numbers of the form p − 1

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Abstract

An asymptotic formula is proved for the sum of values of the Euler function on numbers of the form p − 1 not exceeding x. The order of the remainder of the asymptotics corresponds to the modern bound for zeros of the zeta function.

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References

  1. A. G. Postnikov, Introduction to Analytic Number Theory (Nauka, Moscow, 1971) [in Russian].

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  2. A. A. Karatsuba, Basic Analytic Number Theory, 2nd ed. (Nauka, Moscow, 1983; Springer, 1992).

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  3. G. I. Arkhipov, V. A. Sadovnichii, and V. N. Chubarikov, Lectures in Mathematical Analysis, 3rd ed. (Drofa, Moscow, 2003) [in Russian].

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119899, Russia

    D. V. Goryashin

Authors
  1. D. V. Goryashin
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Additional information

Original Russian Text © D.V. Goryashin, 2009, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2009, Vol. 64, No. 1, pp. 63–65.

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Goryashin, D.V. Summation of the euler function values over numbers of the form p − 1. Moscow Univ. Math. Bull. 64, 41–43 (2009). https://doi.org/10.3103/S0027132209010100

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  • DOI: https://doi.org/10.3103/S0027132209010100

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