On the size of the Gelfond exponent

Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)1056-1060
Number of pages5
JournalJournal of Number Theory
Issue number4
Publication statusPublished - Apr 2010


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