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Bilinear forms with Kloosterman sums and applications
| Content Provider | Semantic Scholar |
|---|---|
| Author | Kowalski, Emmanuel Michel, Ph. Sawin, Will |
| Copyright Year | 2015 |
| Abstract | We prove non-trivial bounds for general bilinear forms in hyper-Kloosterman sums when the sizes of both variables may be below the P\'olya-Vinogradov range. We then derive applications to the second moment of holomorphic cusp forms twisted by characters modulo primes, and to the distribution in arithmetic progressions to large moduli of certain Eisenstein-Hecke coefficients on $\GL_3$. Our main tools are new bounds for certain complete sums in three variables over finite fields, proved using methods from algebraic geometry, especially $\ell$-adic cohomology and the Riemann Hypothesis. |
| Starting Page | 413 |
| Ending Page | 500 |
| Page Count | 88 |
| File Format | PDF HTM / HTML |
| DOI | 10.4007/annals.2017.186.2.2 |
| Alternate Webpage(s) | https://people.math.ethz.ch/~kowalski/bilinearforms.pdf |
| Alternate Webpage(s) | https://arxiv.org/pdf/1511.01636v5.pdf |
| Alternate Webpage(s) | https://doi.org/10.4007/annals.2017.186.2.2 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
