Bounds of multiplicative character sums with Fermat quotients of primes

Igor E. Shparlinski

doi:10.1017/S000497271000198X

Bounds of multiplicative character sums with Fermat quotients of primes

Igor E. Shparlinski

School of Computing

Research output: Contribution to journal › Article › peer-review

29 Citations (Scopus)

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Abstract

Given a prime p, the Fermat quotient q_p(u) of u with gcd (u,p)=1 is defined by the conditions q_p(u) ≡ u^p-1-1/p mod p, -< q_p (u) ≤ p -1. We derive a new bound on multiplicative character sums with Fermat quotients q_p(ℓ) at prime argumentsℓ.

Original language	English
Pages (from-to)	456-462
Number of pages	7
Journal	Bulletin of the Australian Mathematical Society
Volume	83
Issue number	3
DOIs	https://doi.org/10.1017/S000497271000198X
Publication status	Published - Jun 2011

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title = "Bounds of multiplicative character sums with Fermat quotients of primes",

abstract = "Given a prime p, the Fermat quotient qp(u) of u with gcd (u,p)=1 is defined by the conditions qp(u) ≡ up-1-1/p mod p, -< qp (u) ≤ p -1. We derive a new bound on multiplicative character sums with Fermat quotients qp(ℓ) at prime argumentsℓ.",

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AB - Given a prime p, the Fermat quotient qp(u) of u with gcd (u,p)=1 is defined by the conditions qp(u) ≡ up-1-1/p mod p, -< qp (u) ≤ p -1. We derive a new bound on multiplicative character sums with Fermat quotients qp(ℓ) at prime argumentsℓ.

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JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

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Bounds of multiplicative character sums with Fermat quotients of primes

Abstract

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