cusp form

A cusp formMathworldPlanetmathPlanetmath is a modular formMathworldPlanetmath whose first coefficient in any expansion around a cusp is zero. Another more general way to define cusp forms is to consider the forms orthogonalMathworldPlanetmathPlanetmath to Eisenstein seriesMathworldPlanetmath with respect to the Petersson scalar productMathworldPlanetmath.

The Weierstrass Δ functionMathworldPlanetmath, also called modular discriminantMathworldPlanetmath is a weight 12 cusp form for the full modular group SL2()

Δ(z)=qn=1(1-qn)24 (1)

The vector spaceMathworldPlanetmath of weight k cusp forms for the full modular group is finite dimensionnal and non-trivial for k integral greater than 12 and not 14.

Title cusp form
Canonical name CuspForm
Date of creation 2013-03-22 14:07:43
Last modified on 2013-03-22 14:07:43
Owner olivierfouquetx (2421)
Last modified by olivierfouquetx (2421)
Numerical id 9
Author olivierfouquetx (2421)
Entry type Definition
Classification msc 11F11