Results 21 to 30 of about 10,606 (255)
sl(2)ˆ decomposition of denominator formulae of some BKM Lie superalgebras
Nuclear Physics B, 2021 We study a family of Siegel modular forms that are constructed using Jacobi forms that arise in Umbral moonshine. All but one of them arise as the Weyl-Kac-Borcherds denominator formula of some Borcherds-Kac-Moody (BKM) Lie superalgebras.
Suresh Govindarajan +2 more
doaj +1 more source
4-manifolds and topological modular forms
Journal of High Energy Physics, 2021 We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1, 0) theories on 4-manifolds with flavor symmetry backgrounds.
Sergei Gukov +3 more
doaj +1 more source
Mathieu moonshine and Siegel Modular Forms
Journal of High Energy Physics, 2021 A second-quantized version of Mathieu moonshine leads to product formulae for functions that are potentially genus-two Siegel Modular Forms analogous to the Igusa Cusp Form. The modularity of these functions do not follow in an obvious manner.
Suresh Govindarajan, Sutapa Samanta
doaj +1 more source
Interpolated Sequences and Critical L-Values of Modular Forms
, 2021 Recently, Zagier expressed an interpolated version of the Apéry numbers for (3) in terms of a critical L-value of a modular form of weight 4. We extend this evaluation in two directions.
Straub, Armin, Osburn, Robert
core +1 more source
The module of vector-valued modular forms is Cohen-Macaulay [PDF]
, 2020 summary:Let $H$ denote a finite index subgroup of the modular group $\Gamma $ and let $\rho $ denote a finite-dimensional complex representation of $H.$ Let $M(\rho )$ denote the collection of holomorphic vector-valued modular forms for $\rho $ and let ...
Gottesman, Richard
core +1 more source
Constructing modular forms from harmonic Maass Jacobi forms [PDF]
, 2021 summary:We construct a family of modular forms from harmonic Maass Jacobi forms by considering their Taylor expansion and using the method of holomorphic projection.
Zhou, Haigang, Xiong, Ran
core +1 more source
Meromorphic modular forms and the three-loop equal-mass banana integral
Journal of High Energy Physics, 2022 We consider a class of differential equations for multi-loop Feynman integrals which can be solved to all orders in dimensional regularisation in terms of iterated integrals of meromorphic modular forms.
Johannes Broedel +2 more
doaj +1 more source
Modular graph forms from equivariant iterated Eisenstein integrals
Journal of High Energy Physics, 2022 The low-energy expansion of closed-string scattering amplitudes at genus one introduces infinite families of non-holomorphic modular forms called modular graph forms.
Daniele Dorigoni +7 more
doaj +1 more source
Modular Forms on Hecke's Modular Groups [PDF]
Proceedings of the American Mathematical Society, 1973 Let H={-r=x+iy:y>0}. Let A>0, k>O, y=I1. Let M(Q, k, y) denote the set of functions f for which f(r)= .D=o ane2'i"rli and f(-1/T)=y(&/i)kf(T), for all T r H. Let MO(A, k, y) denote the set of feM(A, k. y) for which f((T)=O(yc) uniformly for all x as y-+, for some real c.
openaire +2 more sources
Neutrino masses and mixing from double covering of finite modular groups
Journal of High Energy Physics, 2019 We extend the even weight modular forms of modular invariant approach to general integral weight modular forms. We find that the modular forms of integral weights and level N can be arranged into irreducible representations of the homogeneous finite ...
Xiang-Gan Liu, Gui-Jun Ding
doaj +1 more source