Results 41 to 50 of about 378,592 (232)
Journal of Mathematical Analysis and Applications, 1974 The Fourier coefficients of certain automorphic forms are evaluated using a tensor product construction appearing in a formal proof of the Ramanujan hypothesis [ 11. Let r be the set of two-by-two matrices with integer entries and positive determinant. The modular group is the set of elements of I’ of determinant one. A subgroup of the modular group is
openaire +2 more sources
Poincaré series for modular graph forms at depth two. Part II. Iterated integrals of cusp forms
Journal of High Energy Physics, 2022 We continue the analysis of modular invariant functions, subject to inhomogeneous Laplace eigenvalue equations, that were determined in terms of Poincaré series in a companion paper. The source term of the Laplace equation is a product of (derivatives of)
Daniele Dorigoni +2 more
doaj +1 more source
sl(2)ˆ Decomposition of denominator formulae of some BKM Lie superalgebras - II
Nuclear Physics B, 2023 The square-root of Siegel modular forms of CHL ZN orbifolds of type II compactifications are denominator formulae for some Borcherds-Kac-Moody Lie superalgebras for N=1,2,3,4.
Suresh Govindarajan, Mohammad Shabbir
doaj +1 more source
Journal of Algebra, 1986 Let S(N,k,\(\epsilon)\) denote the space of cusp forms of weight k, level N, and character \(\epsilon\). The theory of newforms describes the structure of S(N,k,\(\epsilon)\). This paper gives a sharper result in this direction. For each prime q dividing N, an operator \(C_ q\), arising from the familiar \(U_ q\) and the Atkin-Lehner \(W_ q\) operator,
openaire +3 more sources
Hecke operators on Hilbert-Siegel modular forms
, 2007 We define Hilbert-Siegel modular forms and Hecke "operators" acting on them. As with Hilbert modular forms, these linear transformations are not linear operators until we consider a direct product of spaces of modular forms (with varying groups), modulo ...
Caulk, Suzanne, Walling, Lynne H.
core +1 more source
On the normalisation of the modular forms in modular invariant theories of flavour
Physics Letters BThe problem of normalisation of the modular forms in modular invariant lepton and quark flavour models is discussed. Modular invariant normalisations of the modular forms are proposed.
S.T. Petcov
doaj +1 more source
Flux vacua and modularity for $\mathbb{Z}_2$ symmetric Calabi-Yau manifolds
SciPost Physics, 2023 We find continuous families of supersymmetric flux vacua in IIB Calabi-Yau compactifications for multiparameter manifolds with an appropriate $\mathbb{Z}_{2}$ symmetry.
Philip Candelas, Xenia de la Ossa, Pyry Kuusela, Joseph McGovern
doaj +1 more source
, 2010 We define two-parameter generalizations of Andrews' $(k+1)$-marked odd Durfee symbols and $2k$th symmetrized odd rank moments, and study the automorphic properties of some of their generating functions.
Andrews +8 more
core +1 more source
Multiplying Modular Forms [PDF]
, 2008 The space of elliptic modular forms of fixed weight and level can be identfied with a space of intertwining operators, from a holomorphic discrete series representation of SL2(R) to a space of automorphic forms. Moreover, multiplying elliptic modular forms corresponds to a branching problem involving tensor products of holomorphic discrete series ...
openaire +3 more sources
ρ — Adic Analogues of Ramanujan Type Formulas for 1/π
Mathematics, 2013 Following Ramanujan’s work on modular equations and approximations of π, there are formulas for 1/π of the form [PLEASE CHECK FORMULA IN THE PDF] for d = 2, 3, 4, 6, where λd are singular values that correspond to elliptic curves with complex ...
Sarah Chisholm +4 more
doaj +1 more source