Delta form: Difference between revisions
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In [[mathematics]], '''Delta''' is a [[modular form]], arising from the [[discriminant of an elliptic curve]]. As a modular form it is a [[cusp form]] of [[weight of a modular form|weight]] 12 and [[level of a modular form|level]] 1 for the full [[modular group]]. It is an [[eigenform]] for the [[Hecke algebra]]. | In [[mathematics]], '''Delta''' is a [[modular form]], arising from the [[discriminant of an elliptic curve]]. As a modular form it is a [[cusp form]] of [[weight of a modular form|weight]] 12 and [[level of a modular form|level]] 1 for the full [[modular group]]. It is an [[eigenform]] for the [[Hecke algebra]]. | ||
Revision as of 16:46, 3 December 2008
In mathematics, Delta is a modular form, arising from the discriminant of an elliptic curve. As a modular form it is a cusp form of weight 12 and level 1 for the full modular group. It is an eigenform for the Hecke algebra.
The q-expansion is
where τ is Ramanujan's tau function. Since Δ is a Hecke eigenform, the tau function is multiplicative.
Dedekind's eta function is a 24-th root of Δ.