Uniformization and Constructive Analytic Continuation of Taylor Series

Distributions and Analytic Continuation of Dirichlet Series

Dirichlet series and Fourier series can both be used to encode sequences of complex numbers an , n ∈ N. Dirichlet series do so in a manner adapted to the multiplicative structure of N, whereas Fourier series reflect the additive structure of N. Formally at least, the Mellin transform relates these two ways of representing sequences. In this paper, we make sense of the Mellin transform of period...

The Analytic Continuation of the Discrete Series

In this paper the analytic continuation of the holomorphic discrete series is defined. The most elementary properties of these representations are developed. The study of when these representations are unitary is begun.

Analytic Continuation of the Fibonacci Dirichlet Series

Functions defined by Dirichlet series J^=l a/f are Interesting because they often code and link properties of an algebraic nature in analytic terms. This is most often the case when the coefficients an are multiplicative arithmetic functions, such as the number or sum of the divisors of w, or group characters. Such series were the first to be studied, and are fundamental in many aspects of numb...

Analytic Continuation of the Principal Series

The purpose of this note is to announce results obtained in the analytic continuation of the (nondegenerate) "principal series" of representations of the nXn complex unimodular group. This study has as its starting point a similar one for the 2X2 real unimodular group previously carried out by us in [4]. We let G be the nXn complex unimodular group and C its diagonal subgroup consisting of elem...

Analytic Continuation for Cubic Multiple Dirichlet Series