Results 21 to 30 of about 464,694 (290)
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
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Proof of a modular relation between 1-, 2- and 3-loop Feynman diagrams on a torus [PDF]
, 2015 The coefficients of the higher-derivative terms in the low energy expansion of genus-one graviton Type II superstring scattering amplitudes are determined by integrating sums of non-holomorphic modular functions over the complex structure modulus of a ...
D'Hoker, Eric +2 more
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Modular divisor functions and quadratic reciprocity [PDF]
, 2010 It is a well-known result by B. Riemann that the terms of a conditionally convergent series of real numbers can be rearranged in a permutation such that the resulting series converges to any prescribed sum s: add p1 consecutive positive terms until their
Steiner, R.
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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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Higher Coxeter graphs associated to affine su(3) modular invariants [PDF]
, 2005 The affine $su(3)$ modular invariant partition functions in 2d RCFT are associated with a set of generalized Coxeter graphs. These partition functions fall into two classes, the block-diagonal (Type I) and the non block-diagonal (Type II) cases ...
Hammaoui, D., Schieber, G., Tahri, E. H.
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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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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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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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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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On the modular invariance of mass eigenstates and CP violation [PDF]
, 2001 We investigate the modular transformation properties of observable (light) fields in heterotic orbifolds, in the light of recent calculations of CP-violating quantities.
Dent, Thomas
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