Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415676 | Journal of Number Theory | 2011 | 6 Pages |
Abstract
We prove two identities involving Dirichlet series, in the denominators of whose terms sums of two, three and four squares appear. These follow from two classical identities of Jacobi involving the four Jacobian Theta Functions θ1(z;q), θ2(z;q), θ3(z;q) and θ4(z;q), by the application of the Mellin transform. These results motivate the well-known correspondence between the set of the four Jacobian Theta Functions and the set of four classical zeta functions of which the Riemann Zeta Function is the third, and the Dirichlet Beta Function is the first.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Somjit Dutt,