Character sums with exponential functions over smooth numbers

On Certain Character Sums over Smooth Numbers

Character Sums with Exponential Functions and their Applications

A catalogue record of this book is available from the British Library Library of Congress Cataloguing in Publication data Kon iagin, S. V. (Sergeˇı Vladimirovich) Character sums with exponential functions and their applications

Bilinear Sums with Exponential Functions

Let g = 0,±1 be a fixed integer. Given two sequences of complex numbers (φm) ∞ m=1 and (ψn) ∞ n=1 and two sufficiently large integers M and N , we estimate the exponential sums ∑ p≤M gcd(ag,p)=1 ∑ 1≤n≤N φpψnep (ag ) , a ∈ Z, where the outer summation is taken over all primes p ≤ M with gcd(ag, p) = 1.

Upper bound estimate of character sums over Lehmer's numbers

*Correspondence: [email protected] Department of Mathematics, Northwest University, Xi’an, Shaanxi, P.R. China Abstract Let p be an odd prime. For each integer awith 1≤ a≤ p – 1, it is clear that there exists one and only one awith 0≤ a≤ p – 1 such that a · a≡ 1 mod p. LetA denote the set of all integers 1≤ a≤ p – 1, in which a and a are of opposite parity. The main purpose of this paper is us...

Sums and products with smooth numbers

Article history: Received 22 September 2010 Accepted 2 November 2010 Available online 12 February 2011 Communicated by Robert C. Vaughan MSC: 11B75 11N25