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- Brandes, JuliaGothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg (author)
On generating functions in additive number theory, II: lower-order terms and applications to PDEs
- Article/chapterEnglish2021
Publisher, publication year, extent ...
- 2020-12-23
- Springer Science and Business Media LLC,2021
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- LIBRIS-ID:oai:gup.ub.gu.se/300964
- https://gup.ub.gu.se/publication/300964URI
- https://doi.org/10.1007/s00208-020-02107-0DOI
- https://research.chalmers.se/publication/521868URI
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- Language:English
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Notes
- We obtain asymptotics for sums of the form Sigma(p)(n=1) e(alpha(k) n(k) + alpha(1)n), involving lower order main terms. As an application, we show that for almost all alpha(2) is an element of [0, 1) one has sup(alpha 1 is an element of[0,1)) | Sigma(1 <= n <= P) e(alpha(1)(n(3) + n) + alpha(2)n(3))| << P3/4+epsilon, and that in a suitable sense this is best possible. This allows us to improve bounds for the fractal dimension of solutions to the Schrodinger and Airy equations.
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- NATURVETENSKAP Matematik hsv//swe
- NATURAL SCIENCES Mathematics hsv//eng
- NATURVETENSKAP Matematik Beräkningsmatematik hsv//swe
- NATURAL SCIENCES Mathematics Computational Mathematics hsv//eng
- NATURVETENSKAP Matematik Diskret matematik hsv//swe
- NATURAL SCIENCES Mathematics Discrete Mathematics hsv//eng
- NATURVETENSKAP Matematik Matematisk analys hsv//swe
- NATURAL SCIENCES Mathematics Mathematical Analysis hsv//eng
- main conjecture
- Mathematics
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- Parsell, S. T.West Chester University (author)
- Poulias, C.University of Bristol (author)
- Shakan, G.University Of Oxford (author)
- Vaughan, R. C.Pennsylvania State University (author)
- Göteborgs universitetInstitutionen för matematiska vetenskaper (creator_code:org_t)
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- In:Mathematische Annalen: Springer Science and Business Media LLC379, s. 347-760025-58311432-1807
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