Author

Igor E. Shparlinski

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Preprint Oct 2026

Systems of equations with elements of finitely generated groups and with linear recurrence sequences

We obtain new and essentially optimal bounds on the number of solutions of diagonal systems of $k$ polynomial equations in $s$ variables from an arbitrary finite subset of a finitely generated group in a field of characteristic zero. Our bounds generalise and sometimes improve previous results of J. Bourgain, M. Z. Gar...

Subham Bhakta, Alina Ostafe, Igor E. Shparlinski · 0 citations

Preprint Sep 2026

Counting consecutive multiplicatively dependent triples

We obtain a nontrivial bound on the number of triples of positive integers $(a,b,c) \in [1,H]^3$, which are multiplicatively dependent but each pair of its elements is not, and so is the triple $ (a+1,b+1,c+1)$. The method is based on studying factorisations of some resultants and a recent improvement by G. Binyamini,...

Igor E. Shparlinski, Nicolas Sleiman · 0 citations