Скачать или смотреть Probabilistic Number Theory: L08 - Dirichlet series and Euler products

Title: Dirichlet series and Euler products

Abstract: The primary goal of this lecture is to understand how nicely a Dirichlet series corresponding to arithmetic functions behaves in the region where it is absolutely convergent. We discuss some important properties of Dirichlet series in their half-plane of absolute convergence. We also show that the Dirichlet series of a multiplicative function can be written as an Euler product in the region where the series is absolutely convergent. Finally, we introduce the notion of the Dirichlet convolution of two arithmetic functions and the product of Dirichlet series. We then discuss a few examples.

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