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ON SEMIGROUP ORBITS OF POLYNOMIALS AND MULTIPLICATIVE ORDERS

Published online by Cambridge University Press:  20 February 2020

JORGE MELLO
Affiliation:
School of Mathematics and Statistics,University of New South Wales, Kensington, NSW 2052, Australia email j.mello@unsw.edu.au
Corresponding
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Abstract

We show, under some natural restrictions, that some semigroup orbits of polynomials cannot contain too many elements of small multiplicative order modulo a large prime $p$ , extending previous work of Shparlinski [‘Multiplicative orders in orbits of polynomials over finite fields’, Glasg. Math. J.60(2) (2018), 487–493].

Type
Research Article
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

For this research, the author was supported by the Australian Research Council Grant DP180100201.

References

Mello, J., ‘On quantitative estimates for quasiintegral points in orbits of semigroups of rational maps’, New York J. Math. 25 (2019), 10911111.Google Scholar
Mérai, L. and Shparlinski, I. E., ‘Unlikely intersections over finite fields: polynomial orbits in small subgroups’, Preprint, 2019, arXiv:1904.12621.Google Scholar
Ostafe, A. and Shparlinski, I. E., ‘Orbits of algebraic dynamical systems in subgroups and subfields’, in: Number Theory—Diophantine Problems, Uniform Distribution and Applications (eds. Elsholtz, C. and Grabner, P.) (Springer, Cham, 2017), 347368.CrossRefGoogle Scholar
Ostafe, A. and Young, M., ‘On algebraic integers of bounded house and preperiodicity in polynomial semigroup dynamics’, Preprint, 2018, arXiv:1807.11645.CrossRefGoogle Scholar
Shparlinski, I. E., ‘Multiplicative orders in orbits of polynomials over finite fields’, Glasg. Math. J. 60(2) (2018), 487493.CrossRefGoogle Scholar

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ON SEMIGROUP ORBITS OF POLYNOMIALS AND MULTIPLICATIVE ORDERS
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