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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/24183
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- Title
- Exponential sums over Mersenne numbers
- Related
- Compositio mathematica, Vol. 140, Issue 1, p.15-30
- DOI
- 10.1112/S0010437X03000022
- Publisher
- London Mathematical Society
- Date
- 2004
- Author/Creator
- Banks, William D
- Author/Creator
- Conflitti, Alessandro
- Author/Creator
- Friedlander, John B
- Author/Creator
- Shparlinski, Igor E
- Description
- We give estimates for exponential sums of the form ∑n≤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 ∑p≤N exp(2πiaMp/m), where Mp is the Mersenne number; Mp = 2[p] −1 for any prime p.We also estimate some closely related sums, including ∑n≤N μ(n) exp(2πiagⁿ/m) and ∑n≤N μ²(n) exp(2πiagⁿ/m), where μ is the Möbius function.
- Description
- 16 page(s)
- Subject Keyword
- 010100 Pure Mathematics
- Subject Keyword
- exponential sums over primes
- Subject Keyword
- Mersenne numbers
- Resource Type
- journal article
- Organisation
- Macquarie University. Department of Computing
- Identifier
- http://hdl.handle.net/1959.14/24183
- Identifier
- mq:3287
- Identifier
- ISSN:1570-5846
- Identifier
- mq-rm-2004021794
- Language
- eng
- Reviewed
Macquarie University ResearchOnline
