Kloosterman sums with primes to composite moduli

2019/11/22 by Korolev, M. A.
#11A07 #11L05 #11L07 #11L20 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1911.09981

Abstract

We obtain a new estimate for Kloosterman sum with primes p\leqslant X to composite modulo q, that is, for the exponential sum of the type ∑_{p\leqslant X, p \nmid q}exp\biggl((2πi)/(q)(ap+bp) \biggr), (ab,q)=1, pp≡ 1\pmodq, which is non-trivial in the case when q ^3/4+ε\leqslant X≪ q ^3/2. We also apply this estimate to the proof of solvability of some congruences with inverse prime residues \pmodq.

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