Back to Search
Start Over
Large Weyl sums and Hausdorff dimension
- Publication Year :
- 2021
-
Abstract
- We obtain the exact value of the Hausdorff dimension of the set of coefficients of Gauss sums which for a given $\alpha \in (1/2,1)$ achieve the order at least $N^{\alpha}$ for infinitely many sum lengths $N$. For Weyl sums with polynomials of degree $d\ge 3$ we obtain a new upper bound on the Hausdorff dimension of the set of polynomial coefficients corresponding to large values of Weyl sums. Our methods also work for monomial sums, match the previously known lower bounds, just giving exact value for the corresponding Hausdorff dimension when $\alpha$ is close to $1$. We also obtain a nearly tight bound in a similar question with arbitrary integer sequences of polynomial growth.<br />Comment: 51 pages, 0 figures
- Subjects :
- Mathematics - Number Theory
Mathematics - Classical Analysis and ODEs
11L15, 11K55
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2108.10439
- Document Type :
- Working Paper