Dirichlet polynomials: some old and recent results, and their interplay in number theory

Abstract

In the first part of this expository paper, we present and discuss the interplay of Dirichlet polynomials in some classical problems of number theory, notably the Lindelöf Hypothesis. We review some typical properties of their means and continue with some investigations concerning their supremum properties. Their random counterpart is considered in the last part of the paper, where a analysis of their supremum properties, based on methods of stochastic processes, is developed.

29 pages

References in corpus (4)

• Sampling the Lindelöf Hypothesis with the Cauchy Random Walk
• On localization in Kronecker's diophantine theorem
• Supremum of Random Dirichlet Polynomials with Sub-multiplicative Coefficients
• Loop coproducts