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 -