L-functions and higher order modular forms

Research paper by David W. Farmer, Sarah Zubairy

Indexed on: 07 Jan '06Published on: 07 Jan '06Published in: Mathematics - Number Theory


It is believed that Dirichlet series with a functional equation and Euler product of a particular form are associated to holomorphic newforms on a Hecke congruence group. We perform computer algebra experiments which find that in certain cases one can associate a kind of ``higher order modular form'' to such Dirichlet series. This suggests a possible approach to a proof of the conjecture.