Published May 23, 2022
| Published
Journal Article
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Moment estimates for the exponential sum with higher divisor functions
- Creators
- Pandey, Mayank
Chicago
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Abstract
For a sequence (a_n)_(n⩾1) of arithmetic interest, it is often desirable to have estimates for the L^p norms of the exponential sum M(α) = Σ_(n⩽X) a_ne(nα) as X grows. Such estimates are useful in applications of the circle method. In addition, sufficiently strong estimates for them can yield estimates for the distribution function {α ∈ [0,1] : |M(α)|⩾ λ} for λ in appropriate ranges.
Additional Information
This article is licensed under the Creative Commons Attribution 4.0 International License. The author would like to thank the anonymous referee for various corrections as well as for pointing out the simplified decomposition into type I and II sums used in the proof of Proposition 4.Attached Files
Published - CRMATH_2022__360_G5_419_0.pdf
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CRMATH_2022__360_G5_419_0.pdf
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Additional details
- Eprint ID
- 118271
- Resolver ID
- CaltechAUTHORS:20221208-566252400.1
- Created
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2023-01-10Created from EPrint's datestamp field
- Updated
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2023-04-23Created from EPrint's last_modified field