Nature

Modular Forms And Conformal Field Theory

Modular forms provide a powerful mathematical framework for understanding symmetry in two-dimensional quantum field theories. In conformal field theory (CFT), these holomorphic functions obey ...
JSTOR Daily

VECTOR-VALUED MODULAR FORMS ON A THREE-DIMENSIONAL BALL

In this paper we give a structure theorem for the module of vector valued modular forms in the case of a three dimensional ball with the action of the Picard modular group Γ 3 [ −2 ] . The ...
GitHub

modular_forms_and_hecke_operators.rst

A congruence subgroup is a subgroup of the group \mathrm{SL}_2(\ZZ) of determinant \pm 1 integer matrices that contains \Gamma(N) = \mathrm{Ker}(\mathrm{SL}_2(\ZZ) \to \mathrm{SL}_2(\ZZ/N\ZZ)) We can ...
JSTOR Daily

ON THE FOURIER COEFFICIENTS OF HILBERT MODULAR FORMS OF HALF-INTEGRAL WEIGHT OVER ARBITRARY ALGEBRAIC NUMBER FIELDS

Tsukuba Journal of Mathematics, Vol. 37, No. 1 (July 2013), pp. 1-11 (11 pages) In Theorem 2.5 in previous paper [4], we determined the Fourier coefficients of the image of Shimura correspondence of ...
RealClearScience

Modular Forms: Math's 'Fifth Fundamental Operation'

“There are five fundamental operations in mathematics,” the German mathematician Martin Eichler supposedly said. “Addition, subtraction, multiplication, division and modular forms.” Part of the joke, ...