Journal article
Metric theory of Weyl sums
- Abstract:
-
We prove that there exist positive constants C and c such that for any integer d⩾ 2 the set of x∈ [0 , 1) d satisfying cN1/2⩽|∑n=1Nexp(2πi(x1n+…+xdnd))|⩽CN1/2for infinitely many natural numbers N is of full Lebesque measure. This substantially improves the previous results where similar sets have been measured in terms of the Hausdorff dimension. We also obtain similar bounds for exponential sums with monomials xnd when d≠ 4. Finally, we obtain lower bounds for the Hausdorff dimension of large values of general exponential polynomials.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
Actions
Access Document
- Files:
-
-
(Preview, Accepted manuscript, pdf, 623.0KB, Terms of use)
-
- Publisher copy:
- 10.1007/s00208-021-02352-x
Authors
- Publisher:
- Springer
- Journal:
- Mathematische Annalen More from this journal
- Volume:
- 385
- Pages:
- 309-355
- Publication date:
- 2022-01-05
- Acceptance date:
- 2021-12-17
- DOI:
- EISSN:
-
1432-1807
- ISSN:
-
0025-5831
- Language:
-
English
- Keywords:
- Pubs id:
-
1232193
- Local pid:
-
pubs:1232193
- Deposit date:
-
2022-01-14
Terms of use
- Copyright holder:
- Chen et al.
- Copyright date:
- 2022
- Rights statement:
- Copyright © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature
- Notes:
-
This is the accepted manuscript version of the article. The final version is available from Springer at https://doi.org/10.1007/s00208-021-02352-x
If you are the owner of this record, you can report an update to it here: Report update to this record