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Sums of Values of Nonprincipal Characters over Shifted Primes

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Irregularities in the Distribution of Prime Numbers

Abstract

For a nonprincipal character χ modulo D, when \(x\ge D^{\frac {5}{6}+\varepsilon }\), (l, D) = 1, we prove a nontrivial estimate of the form \(\sum _{n\le x}\varLambda (n)\chi (n-l)\ll x\exp \left (-0.6\sqrt {\ln D}\right )\) for the sum of values of χ over a sequence of shifted primes.

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Authors and Affiliations

  1. A. Juraev Institute of Mathematics, Academy of Sciences of the Republic of Tajikistan, Dushanbe, Tajikistan

    Zarullo Rakhmonov

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  1. Zarullo Rakhmonov
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Correspondence to Zarullo Rakhmonov .

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Editors and Affiliations

  1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

    János Pintz

  2. Institute of Mathematics, University of Zürich, Zürich, Switzerland

    Michael Th. Rassias

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Rakhmonov, Z. (2018). Sums of Values of Nonprincipal Characters over Shifted Primes. In: Pintz, J., Rassias, M. (eds) Irregularities in the Distribution of Prime Numbers. Springer, Cham. https://doi.org/10.1007/978-3-319-92777-0_10

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