# The general theory of Dirichlet's series

@article{HardyTheGT, title={The general theory of Dirichlet's series}, author={Gordon H. Hardy}, journal={The Mathematical Gazette}, volume={8}, pages={307 - 308} }

V The Fundamental Properties of Analyt'ic Functions ; Taylor's, Latirent's, and Liouville's Theorems ; VI. The Theory of Residues ; Application to the Evaluation of Definite Integrals ; VIL. The Expansion of Functions in Infinite Series ; VIII. Asyrnptotie Expansions and Summnble Serics ; IX. Fourier Series ; X. Linear Differential Equations ; XI. Integral Equations. Part 11. Tlle Transcendental Functions. XII. The Gamma Fllnctiorl ; XIII . The Zeta Function of Rienlann ; XIV Tlle…

## 285 Citations

### Foundations of the theory of Dirichlet series

- Mathematics
- 1967

1. A modern reader, familiar with the methods of functional analysis, is struck with the conviction tha t the classical theory of Dirichlet series [3, 5, 6] must have content expressible in more…

### ANALYTIC CONTINUATION OF THE FIBONACCI DIRICHLET SERIES

- Mathematics
- 2001

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…

### A Jentzsch-Theorem for Kapteyn, Neumann and General Dirichlet Series

- MathematicsComputational Methods and Function Theory
- 2022

Comparing phase plots of truncated series solutions of Kepler’s equation by Lagrange’s power series with those by Bessel’s Kapteyn series strongly suggests that a Jentzsch-type theorem holds true not…

### Distributional Asymptotic Expansions of Spectral Functions and of the Associated Green Kernels

- Mathematics
- 1997

Asymptotic expansions of Green functions and spectral densities associated with partial differential operators are widely applied in quantum field theory and elsewhere. The mathematical properties of…

### Local behavior of distributions and applications

- Mathematics
- 2009

This dissertation studies local and asymptotic properties of distributions (generalized functions) in connection to several problems in harmonic analysis, approximation theory, classical real and…

### Some families of Mathieu a-series and alternating Mathieu a-series

- MathematicsAppl. Math. Comput.
- 2006

### On the Non-Trivial Zeros of Dirichlet Functions

- Mathematics
- 2021

The purpose of this research is to extend to the functions obtained by meromorphic continuation of general Dirichlet series some properties of the functions in the Selberg class, which are all…

### Asymptotic Analysis of Regular Sequences

- MathematicsAlgorithmica
- 2019

It is shown that the summatory function of a regular sequence can asymptotically be decomposed as a finite sum of periodic fluctuations multiplied by a scaling factor.

### Conservation of Singularities in Functional Equations Associated to Collatz-Type Dynamical Systems; or, Dreamcatchers for Hydra Maps

- Mathematics
- 2019

It is known that the Collatz Conjecture (and the study of similar maps, here called "Hydra maps") can be stated in terms of solution sets of functional equations; or, equivalently, the fixed points…

### On the Riesz Sums in Number Theory

- Mathematics
- 2015

The Riesz means, or sometimes typical means, were introduced by M. Riesz and have been studied in connection with summability of Fourier series and of Dirichlet series [8] and [11]. In…