19 citations · 31 across the 14 of their papers we have counts for
4 papers · 1 filter
On the Erdős--Odlyzko--Sárközy conjecture for prime-power moduli
William Banks, Igor E. Shparlinski
Erdős, Odlyzko and Sárközy conjectured that every reduced residue class modulo contains a product of two primes not exceeding . O. Klurman, A. P. Mangerel and J. Teräväinen…
Arithmetic structure of -norms of matrices
Igor E. Shparlinski, Yixiu Xiao
For a matrix , we define \[ {\mathcal R}(γ)=a_1^2+a_2^2+a_3^2+a_4^2, \qquad \text{where} \ γ=\begin{pmatrix}a_1&a_2\\ a_3&a_4\end{pmatrix}, \] and l…
Large sieve inequality for sums of Legendre symbols over short intervals
Marc Munsch, Igor Shparlinski, Yu-Chen Sun +1
Using the Burgess bound and the Selberg sieve, we obtain an upper bound for the second moment of sums of Legendre symbols over intervals , with the modulus ranging over primes . Th…
Shifted bilinear sums of Salié sums and the distribution of modular square roots of shifted primes
Igor E. Shparlinski, Yixiu Xiao
We establish various upper bounds on Type-I and Type-II shifted bilinear sums with Salié sums modulo a large prime . We use these bounds to study, for fixed integers $a,b\not \e…