64 citations · 329 across the 206 of their papers we have counts for
261 papers
Mean value theorems for rational exponential sums
Doowon Koh, Igor E. Shparlinski
We obtain finite field analogues of a series of recent results on various mean value theorems for Weyl sums. Instead of the Vinogradov Mean Value Theorem, our results rest on the c…
On the Waring problem with Dickson polynomials modulo a prime
Igor E. Shparlinski, José Felipe Voloch
We improve recent results of D. Gomez and A. Winterhof (2010) and of A. Ostafe and I. E. Shparlinski (2011) on the Waring problem with Dickson polynomials in the case of prime fini…
Estimates for trilinear and quadrilinear character sums
Étienne Fouvry, Igor E. Shparlinski, Ping Xi
We obtain new bounds on some trilinear and quadrilinear character sums, which are non-trivial starting from very short ranges of the variables. An application to an apparently new…
Uniform bounds for the density in Artin's conjecture on primitive roots
Antonella Perucca, Igor E. Shparlinski
We consider Artin's conjecture on primitive roots over a number field , reducing an algebraic number . Under the Generalised Riemann Hypothesis, there is a densit…
Statistics of ranks, determinants and characteristic polynomials of rational matrices
Muhammad Afifurrahman, Vivian Kuperberg, Alina Ostafe +1
We consider the set of matrices with rational entries having numerator and denominator of size at most and obtain upper and lower bounds on the number of such matri…
On the sparsity of non-diagonalisable integer matrices and matrices with a given discriminant
Alina Ostafe, Igor E. Shparlinski
We consider the set of -matrices with integer elements of size at most and obtain upper bounds on the number of matrices from $\mathcal…