On the Analytic Continuation of Dirichlet Series

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...

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...

Analytic Continuation for Cubic Multiple Dirichlet Series

Analytic continuation of Dirichlet-Neumann operators

The analytic dependence of Dirichlet-Neumann operators (DNO) with respect to variations of their domain of definition has been successfully used to devise diverse computational strategies for their estimation. These strategies have historically proven very competitive when dealing with small deviations from exactly solvable geometries, as in this case the perturbation series of the DNO can be e...

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.