In the thirties of last century, I. M. Vinogradov established uniform distribution modulo 1 sequence pα when α is a fixed irrational real number and p runs over primes. particular, he showed that inequality ||pα||≤p−1/5+ε has infinitely prime solutions p, where ||.|| denotes distance to nearest integer. This result subsequently been improved by many authors. The current record due Matomäki (200...

<p style='text-indent:20px;'>Elliptic curve cryptography is based upon elliptic curves defined over finite fields. Operations such require arithmetic the underlying field. In particular, fast implementations of multiplication and squaring field are required for performing efficient cryptography. The present work considers problem obtaining algorithms squaring. From a theoretical point vie...

Abstract The main objective of this article is to study the exponential sums associated Fourier coefficients modular forms supported at numbers having a fixed set prime factors. This achieved by establishing an improvement on Shparlinski’s bound for attached certain linear recurrence sequences over finite fields.