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EXPONENTIAL AND CHARACTER SUMS WITH MERSENNE NUMBERS
Part of
- Exponential sums and character sums
WILLIAM D. BANKS, JOHN B. FRIEDLANDER, MOUBARIZ Z. GARAEV, IGOR E. SHPARLINSKI
Journal:

Journal of the Australian Mathematical Society / Volume 92 / Issue 1 / February 2012

Published online by Cambridge University Press:

26 April 2012, pp. 1-13

Print publication:

February 2012
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We give new bounds on sums of the form ∑ n≤NΛ(n)exp (2πiagn/m) and ∑ n≤NΛ(n)χ(gn+a), where Λ is the von Mangoldt function, m is a natural number, a and g are integers coprime to m, and χ is a multiplicative character modulo m. In particular, our results yield bounds on the sums ∑ p≤Nexp (2πiaMp/m) and ∑ p≤Nχ(Mp) with Mersenne numbers Mp=2p−1, where p is prime.

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EXPONENTIAL AND CHARACTER SUMS WITH MERSENNE NUMBERS