General Dirichlet series, arithmetic convolution equations and Laplace transforms

Trigonometric Series via Laplace Transforms

Costas J. Efthimiou Department of Physics University of Central Florida Orlando, FL 32816 USA Introduction In another NOTE in this MAGAZINE, the author presented a method [2] that uses the Laplace transform and allows one to find exact values for a large class of convergent series of rational terms. Recently, in this MAGAZINE too, Lesko and Smith [3] revisited the method and demonstrated an ext...

Bilateral Laplace Transforms on Time Scales: Convergence, Convolution, and the Characterization of Stationary Stochastic Time Series

The convergence of Laplace transforms on time scales is generalized to the bilateral case. The bilateral Laplace transform of a signal on a time scale subsumes the continuous time bilateral Laplace transform, and the discrete time bilateral z-transform as special cases. As in the unilateral case, the regions of convergence (ROCs) time scale Laplace transforms are determined by the time scale’s ...

Asymptotic Laplace Transforms and Evolution Equations

Summation of Series via Laplace Transforms

We consider a forced differential difference equation and by the use of Laplace Transform Theory generate non-hypergeometric type series which we prove may be expressed in closed form.

Special values of shifted convolution Dirichlet series

In a recent important paper, Hoffstein and Hulse [14] generalized the notion of Rankin-Selberg convolution L-functions by defining shifted convolution L-functions. We investigate symmetrized versions of their functions, and we prove that the generating functions of certain special values are linear combinations of weakly holomorphic quasimodular forms and “mixed mock modular” forms.