A Dirichlet L-function looks like this:

http://en.wikipedia.org/wiki/Dirichlet_L-function

And the related modular form looks something like this:

What about the following:

Mathworld, in the above page, mentions that: “Dirichlet L-series can be written as sums of Lerch transcendents with z a power of e^(2pii/k).”

But an explicit google search for the following **does not** appear to result in much useful things:

**“lerch transcendent” “modular forms” Hecke**. I may generate a video showing the interpolation of for a given Dirichlet character from L-function to modular form shortly.

But, lo, I spoke too soon: THE LERCH ZETA FUNCTION I. ZETA INTEGRALS

Advertisements