Weakly holomorphic modular form information

weakly holomorphic modular form is similar to a holomorphic modular form, except that it is allowed to have poles at cusps. Examples include modular functions...

mathematics, a mock modular form is the holomorphic part of a harmonic weak Maass form, and a mock theta function is essentially a mock modular form of weight 1/2...

called an arithmetic group, a modular form of level Γ {\displaystyle \Gamma } and weight k {\displaystyle k} is a holomorphic function f : H → C {\displaystyle...

{\displaystyle k} to the space M 2 − k ! {\displaystyle M_{2-k}^{!}} of weakly holomorphic modular forms of weight 2 − k . {\displaystyle 2-k.} It was proved by Bruinier...

domain of Γ {\displaystyle \Gamma } . In contrast to modular forms, Maass forms need not be holomorphic. They were studied first by Hans Maass in 1949. The...

specific generalizations of modular forms. The classical candidates are the Hilbert modular forms and Siegel modular forms. These days these are associated...

Mk′(Γ0(N)) is spanned by (weakly holomorphic) eta quotients, and Mk′−k(Γ0(N)) contains an eta quotient ηg. Take a modular form f with weight k that is not...

representation ρ: GR → GL(V), the family (V, ρ ⋅ h) is a holomorphic family of Hodge structures; moreover, it forms a variation of Hodge structure, and X is a finite...

functions were a mystery, but they are now known to be the holomorphic parts of harmonic weak Maass forms. Although there are numerous statements that could have...

as the Dirichlet L-functions) to approximate arbitrary non-vanishing holomorphic functions arbitrarily well. The universality of the Riemann zeta function...

of this restriction is that the Laplace transform of a function is a holomorphic function of the variable s. Unlike the Fourier transform, the Laplace...

were not initially known. Physically, the vertex operators arising from holomorphic field insertions at points in two-dimensional conformal field theory...

which turn out to be a type of modular form, and it is connected more generally to the theory of automorphic forms where it appears on one side of the...

complex fields satisfying a property known as holomorphy, which allows holomorphic quantities to be exactly computed. This makes supersymmetric models useful...

underlying structure of a TQFT is a modular category of representations of a quantum group 1986 Saunders Mac Lane Mathematics, form and function (a foundation...

using the anachronistic names. Deligne's conjecture on 1-motives Goldbach's weak conjecture (proved in 2013) Sensitivity conjecture (proved in 2019) The conjectures...

2nd ed., ISBN 978-0-387-97245-9) Introduction to Elliptic Curves and Modular Forms, Neal I. Koblitz (1993, 2nd ed., ISBN 978-0-387-97966-3) Representations...

Langlands' conjectures by reworking and expanding the classical theory of modular forms and their L-functions through the introduction of representation theory...

of forms. Fujita conjecture regarding the line bundle K M ⊗ L ⊗ m {\displaystyle K_{M}\otimes L^{\otimes m}} constructed from a positive holomorphic line...

compact support are precisely functions on R which are restrictions of holomorphic functions on C satisfying an exponential growth condition | F ( λ ) |...

dimensional vector space over the field. 5.  Zariski's main lemma on holomorphic functions says the n-th symbolic power of a prime ideal in a polynomial...