From the 1 of 10 linked papers with an AI index.
10 papers
Large sieve inequality for sums of Legendre symbols over short intervals
Marc Munsch, Igor Shparlinski, Yu-Chen Sun +1
The paper establishes a nontrivial upper bound for the second moment of sums of Legendre symbols over short intervals using the Burgess bound and Selberg sieve, showing that for mo…
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 \…
On quantum ergodicity for higher dimensional cat maps modulo prime powers
Subham Bhakta, Igor E. Shparlinski
A discrete model of quantum ergodicity of linear maps generated by symplectic matrices modulo an integer , has been studied for and…
Triple sums of Kloosterman sums and the discrepancy of modular inverses
Valentin Blomer, Morten S. Risager, Igor E. Shparlinski
We investigate the distribution of modular inverses modulo positive integers in a large interval. We provide upper and lower bounds for their box, ball and isotropic discrepanc…
On the Dynamical System Generated by the Möbius Transformation at Smooth Times
László Mérai, Igor E. Shparlinski
We study the distribution of the sequence of the first elements of the discrete dynamical system generated by the Möbius transformation over…
On the correlations between character sums of division polynomials under shifts
Subham Bhakta, Igor E. Shparlinski
Let be an elliptic curve over the finite field , and be an -rational point. We study the sums \[ S_{Ï,P}(N,h) = \sum_{n=1}^…