arXiv:1210.1893 [math.NT]AbstractReferencesReviewsResources
The number of roots of polynomials of large degree in a prime field
Published 2012-10-05Version 1
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.
Comments: 16 pages
DOI: 10.1093/imrn/rnt227
Categories: math.NT
Keywords: large degree, prime field, polynomials, satisfy simple differential equations, establish asymptotic upper bounds
Tags: journal article
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