Affiliation:
1. Mathematics Institute University of Warwick Coventry UK
Abstract
AbstractAssuming the Generalised Riemann Hypothesis, we prove a sharp upper bound on moments of shifted Dirichlet L‐functions. We use this to obtain conditional upper bounds on high moments of theta functions. Both of these results strengthen theorems of Munsch, who proved almost sharp upper bounds for these quantities. The main new ingredient of our proof comes from a paper of Harper, who showed the related result for all under the Riemann Hypothesis. Finally, we obtain a sharp conditional upper bound on high moments of character sums of arbitrary length.
Funder
University of Warwick
Engineering and Physical Sciences Research Council
Reference18 articles.
1. ON THE CORRELATION OF SHIFTED VALUES OF THE RIEMANN ZETA FUNCTION
2. High order moments of character sums
3. M. J.Curran Correlations of the Riemann zeta function arXiv:2303.10123 2023.
4. Small Gál sums and applications
5. A. J.Harper Sharp conditional bounds for moments of the Riemann zeta function arXiv:1305.4618 2013.
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1 articles.
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1. BOUNDS FOR MOMENTS OF QUADRATIC DIRICHLET CHARACTER SUMS;Bulletin of the Australian Mathematical Society;2024-05-06