Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
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? – Giovanni De Gaetano May 26 '12 at 16:42
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 $0 \leq \alpha < 1$. – Eugene May 26 '12 at 16:53
I'll just edit it into the question. – Dylan Moreland May 26 '12 at 18:58
@DylanMoreland Oh wow. Thanks again! – Eugene May 26 '12 at 19:04

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.