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math.CO2020
On some polynomial version on the sum-product problem for subgroups
Sofia Aleshina, Ilya Vyugin
We generalize two results about subgroups of multiplicative group of finite field of prime order. In particular, the lower bound on the cardinality of the set of values of polynomi…
math.NT2020
Polynomial Equations in Subgroups and Applications
Sergei V. Konyagin, Igor E. Shparlinski, Ilya V. Vyugin
We obtain a new bound for the number of solutions to polynomial equations in cosets of multiplicative subgroups in finite fields, which generalises previous results of P. Corvaja a…