Elements of large order on varieties over prime finite fields

Mei Chu Chang; Bryce Kerr; Igor E. Shparlinski; Umberto Zannier

doi:10.5802/jtnb.880

Elements of large order on varieties over prime finite fields

Mei Chu Chang, Bryce Kerr, Igor E. Shparlinski, Umberto Zannier

School of Computing

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

Let V be a fixed algebraic variety defined by m polynomials in n variables with integer coefficients. We show that there exists a constant C(V) such that for almost all primes p for all but at most C(V) points on the reduction of V modulo p at least one of the components has a large multiplicative order. This generalises several previous results and is a step towards a conjecture of B. Poonen.

Original language	English
Pages (from-to)	579-593
Number of pages	15
Journal	Journal de Theorie des Nombres de Bordeaux
Volume	26
Issue number	3
DOIs	https://doi.org/10.5802/jtnb.880
Publication status	Published - 2014

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10.5802/jtnb.880

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AB - Let V be a fixed algebraic variety defined by m polynomials in n variables with integer coefficients. We show that there exists a constant C(V) such that for almost all primes p for all but at most C(V) points on the reduction of V modulo p at least one of the components has a large multiplicative order. This generalises several previous results and is a step towards a conjecture of B. Poonen.

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Elements of large order on varieties over prime finite fields

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