Elements of large order on varieties over prime finite fields

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

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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 languageEnglish
Pages (from-to)579-593
Number of pages15
JournalJournal de Theorie des Nombres de Bordeaux
Issue number3
Publication statusPublished - 2014


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