In mathematics, such a sum is known as a generalized Dirichlet series; its use for averaging is known as an Abelian mean.
22.
Generally a Dirichlet series converges if the real part of " s " is greater than a number called the abscissa of convergence.
23.
Furthermore, techniques such as partial summation and Tauberian theorems can be used to get information about the coefficients from analytic information about the Dirichlet series.
24.
Together with his collaborators, Dorian Goldfeld has introduced the theory of multiple Dirichlet series, objects that extend the fundamental Dirichlet series in one variable.
25.
Together with his collaborators, Dorian Goldfeld has introduced the theory of multiple Dirichlet series, objects that extend the fundamental Dirichlet series in one variable.
26.
He is also the author of the book " Modular forms and Dirichlet series " ( W . A . Benjamin, 1969 ).
27.
The ring of formal Dirichlet series over "'C "'is isomorphic to a ring of formal power series in countably many variables.
28.
However, if a Dirichlet series converges and diverges at different points on the same vertical line, then this line must be the line of convergence.
29.
Behind the history was the wish of Chevalley to write proofs for class field theory without using Dirichlet series : in other words to eliminate L-functions.
30.
This opened a field for later research on associated Dirichlet series and automorphic forms, and was a major step in the solution of Kummer's conjecture.
