12 citations · 70 across the 40 of their papers we have counts for
9 papers · 1 filter
Sato--Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height
William D. Banks, Igor E. Shparlinski
We obtain asymptotic formulae for the number of primes for which the reduction modulo of the elliptic curve $$ \E_{a,b} : Y^2 = X^3 + aX + b $$ satisfies certain ``nat…
On the distribution of Kloosterman sums
I. E. Shparlinski
For a prime , we consider Kloosterman sums $$ K_{p}(a) = \sum_{x\in \F_p^*} \exp(2 πi (x + ax^{-1})/p), \qquad a \in \F_p^*, $$ over a finite field of elements. It is well k…
Character sums with Beatty sequences on Burgess-type intervals
William D. Banks, Igor E. Shparlinski
We estimate multiplicative character sums taken on the values of a non-homogeneous Beatty sequence , where , and is irrational. Our bounds…
Distribution of modular inverses and multiples of small integers and the Sato--Tate conjecture on average
I. E. Shparlinski
We show that, for sufficiently large integers and , for almost all the ratios and the products , where , are very uniformly distributed in…
Arithmetic properties of the Ramanujan function
Florian Luca, Igor E Shparlinski
We study some arithmetic properties of the Ramanujan function , such as the largest prime divisor and the number of distinct prime divisors of for…
On a Generalisation of a Lehmer Problem
Igor Shparlinski
We consider a generalisation of the classical Lehmer problem about the distribution of modular inverses in arithmetic progression, introduced by E. Alkan, F. Stan and A. Zaharescu.…