On the size of the Gelfond exponent
The author uses an explicit formula of Shevelev on the best possible exponent in the error term of an asymptotic formula of Gelfond for the number of integers in a given residue class and a given parity on the sum of its binary digits and proves unconditionally that this exponent is small for the majority of all primes. This improves on the work of Shevelev who proved, among other things, a similar result by assuming Artin's conjecture on primitive roots.
scientific article; zbMATH DE number 5690738