Exponential Sums over Mersenne Numbers

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Exponential Sums over Mersenne Numbers

Please use this identifier to cite or link to this item: http://hdl.handle.net/10355/10638

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Title: Exponential Sums over Mersenne Numbers
Author: Banks, William David, 1964-; Conflitti, Alessandro; Friedlander, J. B. (John B.); Shparlinski, Igor E.
Keywords: number theory
Date: 2004
Citation: William D. Banks, Alessandro Conflitti, John B. Friedlander and Igor E. Shparlinski.Compositio Mathematica, vol. 140, issue 1 (2004), pp.15-30.
Abstract: We give estimates for exponential sums of the form Σn≤N Λ(n) exp(2πiagn/m), where m is a positive integer, a and g are integers relatively prime to m, and Λ is the von Mangoldt function. In particular, our results yield bounds for exponential sums of the form Σ p≤N exp(2πiaMp/m), where Mp is the Mersenne number; Mp = 2p −1 for any prime p.We also estimate some closely related sums, including Σn≤N μ(n) exp(2πiagn/m) and Σn≤N μ2(n) exp(2πiagn/m), where μ is the Möbius function.
URI: http://hdl.handle.net/10355/10638

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