Among the topics are quadratic points of classical modular curves, p-adic point counting on singular super-elliptic curves, a vanishing criterion for Dirichlet series
with periodic coefficients, the Sato-Tate conjecture for a Picard curve with a complex multiplication, arithmetic twists with abelian extensions, and transcendental numbers with special values of Dirichlet series
Nakajima, A new expression for the product of the two Dirichlet series
The kernel function can be expressed in Dirichlet Series
This requires the associated multiplicative function, say f(n), to have special enough properties that the associated Dirichlet series
may be analytically continued.
Gunnells, Metaplectic ice, in Multiple Dirichlet Series
, L-Functions, and Automorphic Forms, D.
It is easily seen the Dirichlet series
is absolutely convergent for Rs = [sigma] > 1/6.
Widder (1898-1990) drew material from a course of lectures that he gave now and then at Harvard on Dirichlet series
and Laplace integrals, to explain the Laplace transform for students who have a fundamental knowledge of analysis, though proofs are included for those with only a little such knowledge.
alpha]] ([alpha] [member of] C) forms an Abelian group with the Dirichlet series
multiplication followed by a number of applications.
However, the formula may be used to construct twin prime Dirichlet series
This article presents a new algorithm for nonharmonic signal analysis using Dirichlet series
We attach a Dirichlet series
D(s,f) [Mathematical Expression Omitted] by (2.
s] and essentially those Dirichlet series
where one might expect a Riemann hypothesis.