5 citations · 9 across the 6 of their papers we have counts for
6 papers
The large sieve for modulo primes
M. Z. Garaev
Let be a fixed integer, Let be any strictly increasing sequence of positive integers satisfying In this paper we give a version of the…
Uniform Distribution of Fractional Parts Related to Pseudoprimes
William D. Banks, Moubariz Z. Garaev, Florian Luca +1
We estimate exponential sums with the Fermat-like quotients $$ f_g(n) = \frac{g^{n-1} - 1}{n} \mand h_g(n)=\frac{g^{n-1}-1}{P(n)}, $$ where and are positive integers, i…
New estimates of double trigonometric sums with exponential functions
M. Z. Garaev, A. A. Karatsuba
We establish a new bound for the exponential sum \begin{eqnarray*} \sum_{x\in\mathcal{X}}\Big|\sum_{y\in \mathcal{Y}}γ(y)\exp(2πi a λ^{xy}/p)\Big|, \end{eqnarray*} where is an…
On a symmetric congruence and its applications
M. Z. Garaev, A. A. Karatsuba
For a large integer we obtain an asymptotic formula for the number of solutions of a certain congruence modulo with four variables, where the variables belong to special s…
Exponential Sums and Congruences with Factorials
Moubariz Z. Garaev, Florian Luca, Igor E. Shparlinski
We estimate the number of solutions of certain diagonal congruences involving factorials. We use these results to bound exponential sums with products of two factorials and…
Character Sums and Congruences with n!
Moubariz Z. Garaev, Florian Luca, Igor E. Shparlinski
We estimate character sums with n!, on average, and individually. These bounds are used to derive new results about various congruences modulo a prime p and obtain new information…