Polynomial Equations in Subgroups and Applications

Sergei V. Konyagin (), Igor E. Shparlinski () and Ilya V. Vyugin ()
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Sergei V. Konyagin: Steklov Mathematical Institute
Igor E. Shparlinski: University of New South Wales, Department of Pure Mathematics
Ilya V. Vyugin: Institute for Information Transmission Problems RAS

A chapter in Analysis at Large, 2022, pp 273-297 from Springer

Abstract: Abstract We obtain a new bound for the number of solutions to polynomial equations in cosets of multiplicative subgroups in finite fields, which generalizes previous results of P. Corvaja and U. Zannier (2013). We also obtain a conditional improvement of recent results of J. Bourgain, A. Gamburd, and P. Sarnak (2016) and S. V. Konyagin, S. V. Makarychev, I. E. Shparlinski, and I. V. Vyugin (2019) on the structure of solutions to the reduction of the Markoff equation x2 + y2 + z2 = 3xyz modulo a prime p.

Keywords: Polynomial equation; Markoff equation; Reduction modulo p; 11D79; 11T06 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-05331-3_12

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DOI: 10.1007/978-3-031-05331-3_12

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