Results 11 to 20 of about 378,592 (232)
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
Congruences via modular forms [PDF]
, 2010 We prove two congruences for the coefficients of power series expansions in t of modular forms where t is a modular function. As a result, we settle two recent conjectures of Chan, Cooper and Sica.
Osburn, Robert, Sahu, Brundaban
core +4 more sources
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
Holomorphic almost modular forms [PDF]
, 2003 Holomorphic almost modular forms are holomorphic functions of the complex upper half plane which can be approximated arbitrarily well (in a suitable sense) by modular forms of congruence subgroups of large index in $\SL(2,\ZZ)$.
Marklof, Jens
core +2 more sources
Finite Fields and Their Applications, 2001 The author develops a theory of modular forms for the fractional linear action of \(\Gamma:= \text{GL}(2,K)\) on the ``upper half plane'' \(\Omega:={\mathbf P}^1_K - {\mathbf P}^1(K)\), where \(K\) is a finite field. The theory looks like a shadow of the theory of classical or Drinfeld modular forms and, indeed, occurs naturally as the reduction of the
openaire +2 more sources
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
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
Advances in Mathematics, 2018 The denominator formula for the Monster Lie algebra is the product expansion for the modular function $j(z)-j( )$ given in terms of the Hecke system of $\operatorname{SL}_2(\mathbb Z)$-modular functions $j_n( )$. It is prominent in Zagier's seminal paper on traces of singular moduli, and in the Duncan-Frenkel work on Moonshine.
Bringmann, Kathrin +4 more
openaire +5 more sources
Computing mod ℓ Galois representations associated to modular forms for small primes
AIMS Mathematics, 2023 In this paper, we propose an algorithm for computing mod $ \ell $ Galois representations associated to modular forms of weight $ k $ when $ \ell < k-1 $. We also present the corresponding results for the projective Galois representations. Moreover, we
Peng Tian +2 more
doaj +1 more source