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arXiv · 1210.1893

The number of roots of polynomials of large degree in a prime field

Amit Ghosh·Kenneth Ward
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Abstract

We establish asymptotic upper bounds on the number of zeros modulo $p$ of certain polynomials with integer coefficients, with $p$ prime numbers arbitrarily large. The polynomials we consider have degree of size $p$ and are obtained by truncating certain power series with rational coefficients that satisfy simple differential equations.

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Amit Ghosh, Kenneth Ward. 2012-10-05. The number of roots of polynomials of large degree in a prime field. https://doi.org/10.1093/imrn/rnt227

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