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

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

2009-07-28

arxiv.org/abs/0907.4931v3

Mathematics

Number Theory

29 pages

Scientific paper

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 Lindel\"of 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.

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