Results 21 to 30 of about 480,606 (330)
Tetrahedral modular graph functions
Journal of High Energy Physics, 2017 The low-energy expansion of one-loop amplitudes in type II string theory generates a series of world-sheet integrals whose integrands can be represented by world-sheet Feynman diagrams.
Axel Kleinschmidt, Valentin Verschinin
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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
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Polar harmonic Maass forms and their applications [PDF]
, 2016 In this survey, we present recent results of the authors about non-meromorphic modular objects known as polar harmonic Maass forms. These include the computation of Fourier coefficients of meromorphic modular forms and relations between inner products of
Bringmann, Kathrin, Kane, Ben
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Introductory remarks on complex multiplication
International Journal of Mathematics and Mathematical Sciences, 1982 Complex multiplication in its simplest form is a geometric tiling property. In its advanced form it is a unifying motivation of classical mathematics from elliptic integrals to number theory; and it is still of active interest.
Harvey Cohn
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Axioms, 2013 Recently, the authors have established a large class of modular relations involving the Rogers-Ramanujan type functions J(q) and K(q) of order ten. In this paper, we establish further modular relations connecting these two functions with Rogers-Ramanujan
Nasser Abdo Saeed Bulkhali +1 more
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Weighted modular inequalities for monotone functions
Journal of Inequalities and Applications, 1997 Weight characterizations of weighted modular inequalities for operators on the cone of monotone functions are given in terms of composition operators on arbitrary non-negative functions with changes in weights. The results extend to modular inequalities,
Heinig HP, Kufner A, Drábek P
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Modular graph functions and odd cuspidal functions. Fourier and Poincaré series
Journal of High Energy Physics, 2019 Modular graph functions are SL(2, ℤ)-invariant functions associated with Feynman graphs of a two-dimensional conformal field theory on a torus of modulus τ. For one-loop graphs they reduce to real analytic Eisenstein series. We obtain the Fourier series,
Eric D’Hoker, Justin Kaidi
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Asymptotic expansions, $L$-values and a new Quantum Modular Form [PDF]
, 2013 In 2010 Zagier introduced the notion of a quantum modular form. One of his first examples was the "strange" function $F(q)$ of Kontsevich. Here we produce a new example of a quantum modular form by making use of some of Ramanujan's mock theta functions ...
Costa, Edgar +2 more
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Koshliakov zeta functions I: Modular relations [PDF]
Advances in Mathematics, 2021 34 pages, submitted for publication; comments are ...
Dixit, Atul, Gupta, Rajat
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Lattice realizations of unitary minimal modular invariant partition functions [PDF]
, 1995 The conformal spectra of the critical dilute A-D-E lattice models are studied numerically. The results strongly indicate that, in branches 1 and 2, these models provide realizations of the complete A-D-E classification of unitary minimal modular ...
Andrews G E +13 more
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