35 citations · 42 across the 15 of their papers we have counts for
6 papers · 1 filter
Short sums of the Möbius function over function fields
Etienne Fouvry, Igor E. Shparlinski, Ping Xi
We develop a new method which allows us to estimate, with a power saving, sums of the M{ö}bius function over function fields . The sums run over monic polynomials…
Systems of equations with elements of finitely generated groups and with linear recurrence sequences
Subham Bhakta, Alina Ostafe, Igor E. Shparlinski
We obtain new and essentially optimal bounds on the number of solutions of diagonal systems of polynomial equations in variables from an arbitrary finite subset of a finite…
Tridimensional character sums with polynomial arguments and applications
Étienne Fouvry, Igor E. Shparlinski, Ping Xi
Let be a large prime and a non-trivial Dirichlet character modulo . We study the character sum \[ \sum_{a \sim A} \sum_{b \sim B} \sum_{c \sim C} α(a,b) β(c)χ(f(a) + bc)…
Counting consecutive multiplicatively dependent triples
Igor Shparlinski, Nicolas Sleiman
We obtain a nontrivial bound on the number of triples of positive integers , which are multiplicatively dependent but each pair of its elements is not, and so…
On the generation of multiplicative groups by small primes
Oleksiy Klurman, Igor E. Shparlinski, Joni Teräväinen
Motivated by a question of Regev arising from his improved quantum factoring algorithm, we study how many small primes are needed to generate the group $({\mathbb Z}/q{\mathbb Z})^…
Counting Irreducible polynomials with coefficients from thin subgroups
Alina Ostafe, Igor E. Shparlinski
L. Bary-Soroker and R. Shmueli (2026) have given an asymptotic formula for the number of irreducible polynomials over the finite fields of elements, such that the…