In mathematics, a modular form is a holomorphic function on the complex upper half-plane, H {\displaystyle {\mathcal {H}}} , that roughly satisfies a functional...

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...

Teichmüller modular form is an analogue of a Siegel modular form on Teichmüller space. Ichikawa, Takashi (1994), "On Teichmüller modular forms", Mathematische...

In mathematics, a Hilbert modular form is a generalization of modular forms to functions of two or more variables. It is a (complex) analytic function...

In mathematics, Siegel modular forms are a major type of automorphic form. These generalize conventional elliptic modular forms which are closely related...

In mathematics, a p-adic modular form is a p-adic analog of a modular form, with coefficients that are p-adic numbers rather than complex numbers. Serre...

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

from modular arithmetic. The modular group Γ is the group of fractional linear transformations of the complex upper half-plane, which have the form z ↦...

In mathematics, overconvergent modular forms are special p-adic modular forms that are elements of certain p-adic Banach spaces (usually infinite dimensional)...

Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups. Modular forms are holomorphic...

the ring of modular forms associated to a subgroup Γ of the special linear group SL(2, Z) is the graded ring generated by the modular forms of Γ. The study...

In number theory and algebraic geometry, a modular curve Y(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of...

Modular synthesizers are synthesizers composed of separate modules for different functions. The modules can be connected together by the user to create...

mathematics, almost holomorphic modular forms, also called nearly holomorphic modular forms, are a generalization of modular forms that are polynomials in 1/Im(τ)...

In mathematics, topological modular forms (tmf) is the name of a spectrum that describes a generalized cohomology theory. In concrete terms, for any integer...

announced his proof on 23 June 1993 at a lecture in Cambridge entitled "Modular Forms, Elliptic Curves and Galois Representations". However, in September...

mathematics, a cusp form is a particular kind of modular form with a zero constant coefficient in the Fourier series expansion. A cusp form is distinguished...

sets (in the upper halfplane), and is a modular form of weight 2k for Γ. Note that, when Γ is the full modular group and n = 0, one obtains the Eisenstein...

name comes from the classical name modular group of this group, as in modular form theory. In string theory, modular invariance is an additional requirement...

complex modular forms and the p-adic theory of modular forms. Modular forms are analytic functions, so they admit a Fourier series. As modular forms also...

number theory, the modularity theorem states that elliptic curves over the field of rational numbers are related to modular forms in a particular way...

introduced by Petersson (1930), is a generalization to other modular forms or automorphic forms. The Riemann zeta function and the Dirichlet L-function satisfy...

A modular elliptic curve is an elliptic curve E that admits a parametrization X0(N) → E by a modular curve. This is not the same as a modular curve that...

In mathematics, the modular lambda function λ(τ) is a highly symmetric holomorphic function on the complex upper half-plane. It is invariant under the...

=g_{2}^{3}-27g_{3}^{2}.} The discriminant is a modular form of weight 12 {\displaystyle 12} . That is, under the action of the modular group, it transforms as Δ ( a τ...

In mathematics, Felix Klein's j-invariant or j function is a modular function of weight zero for the special linear group SL ⁡ ( 2 , Z ) {\displaystyle...

the classical elliptic modular form theory, the Hecke operators Tn with n coprime to the level acting on the space of cusp forms of a given weight are...

Yutaka Taniyama suspected a link might exist between elliptic curves and modular forms, two completely different areas of mathematics. Known at the time as...

}^{\infty }e^{2\pi inz\ +\ \pi in^{2}\tau }} which is a kind of modular form called a Jacobi form. This is sometimes written in terms of the nome q = e π i...

mechanics. The demodularized standard form of the Ramanujan's continued fraction unanchored from the modular form is as follows:: H ( q ) G ( q ) = [ 1...