3
$\begingroup$

I was reading this paper, and on the first page they define a cusp form as

$$ f(z) = \sum_{n > -\alpha} a(n) e^{2\pi i (n + \alpha)z}. $$

Is this equivalent to the usual definition of a cusp form

$$ f(z) = \sum_{n = 1}^\infty a(n) q^n. $$ where $q = e^{2\pi iz}$?

Also what is a cusp parameter?

  • 0
    The link to the paper seems to require a password. What is the paper? Otherwise can you tell us what is $\alpha$ and over which set we are summing?2012-05-26
  • 0
    The paper is "Rankin-Selberg method for real analytic cusp forms of arbitrary real weight" by Matthes. It just says that $f$ is a holomorphic cusp form with weight $r$ and cusp parameter $0 \leq \alpha < 1$.2012-05-26
  • 0
    I'll just edit it into the question.2012-05-26
  • 0
    @DylanMoreland Oh wow. Thanks again!2012-05-26

0 Answers 0