Sums of Values of Nonprincipal Characters over Shifted Primes

Zarullo Rakhmonov ()
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Zarullo Rakhmonov: Academy of Sciences of the Republic of Tajikistan, A. Juraev Institute of Mathematics

A chapter in Irregularities in the Distribution of Prime Numbers, 2018, pp 187-217 from Springer

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

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-92777-0_10

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DOI: 10.1007/978-3-319-92777-0_10

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