TY - JOUR

T1 - On the size of the Gelfond exponent

AU - Shparlinski, Igor E.

PY - 2010/4

Y1 - 2010/4

N2 - We use the explicit formula of V. Shevelev for the best possible exponent α (m) in the error term of the asymptotic formula of A.O. Gelfond on the number of positive integers n ≤ x in a given residue class modulo m and a given parity of the sum of its binary digits, to obtain new results about its behaviour. In particular, our result implies thatunder(lim inf, p → ∞) α (p) = 0 where p runs through the set of primes, which has been derived by V. Shevelev from Artin's conjecture.

AB - We use the explicit formula of V. Shevelev for the best possible exponent α (m) in the error term of the asymptotic formula of A.O. Gelfond on the number of positive integers n ≤ x in a given residue class modulo m and a given parity of the sum of its binary digits, to obtain new results about its behaviour. In particular, our result implies thatunder(lim inf, p → ∞) α (p) = 0 where p runs through the set of primes, which has been derived by V. Shevelev from Artin's conjecture.

UR - http://www.scopus.com/inward/record.url?scp=76749151756&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2009.09.005

DO - 10.1016/j.jnt.2009.09.005

M3 - Article

AN - SCOPUS:76749151756

VL - 130

SP - 1056

EP - 1060

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 4

ER -