Exponential sums with consecutive modular roots of an integer

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4 Citations (Scopus)


J. Bourgain and the author have recently estimated exponential sums with consecutive modular roots θ1/n (mod p), where θ is of multiplicative order t ≥ pε modulo a prime p (for some fixed ε > 0) and n runs through the integers in the interval [M + 1, M + N] with gcd(n, t) = 1. However, the saving in that bound against the trivial estimate has not been made explicit. It is shown here that for t ≥ p 1/2+ε one can obtain a fully explicit bound for such exponential sums.

Original languageEnglish
Pages (from-to)207-213
Number of pages7
JournalQuarterly Journal of Mathematics
Issue number1
Publication statusPublished - Mar 2011


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