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 form [17]:
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 seriesWe 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.
