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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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, 2021 We examine several currently used techniques for visualizing complex-valued functions applied to modular forms. We plot several examples and study the benefits and limitations of each technique. We then introduce a method of visualization that can take advantage of colormaps in Python's matplotlib library, describe an implementation, and give more ...
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Bilateral series in terms of mixed mock modular forms
Journal of Inequalities and Applications, 2016 The number of strongly unimodal sequences of weight n is denoted by u ∗ ( n ) $u^{*}(n)$ . The generating functions for { u ∗ ( n ) } n = 1 ∞ $\{u^{*}(n)\}_{n=1}^{\infty}$ are U ∗ ( q ) = ∑ n = 1 ∞ u ∗ ( n ) q n $U^{*}(q)=\sum_{n=1}^{\infty}u^{*}(n)q^{n}$
Bin Chen, Haigang Zhou
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Nadler’s Theorem on Incomplete Modular Space
Mathematics, 2021 This manuscript is focused on the role of convexity of the modular, and some fixed point results for contractive correspondence and single-valued mappings are presented.
Fatemeh Lael +3 more
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Ramanujan and coefficients of meromorphic modular forms [PDF]
, 2016 The study of Fourier coefficients of meromorphic modular forms dates back to Ramanujan, who, together with Hardy, studied the reciprocal of the weight 6 Eisenstein series. Ramanujan conjectured a number of further identities for other meromorphic modular
Bringmann, Kathrin, Kane, Ben
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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
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A characterization of convex φ-functions [PDF]
Opuscula Mathematica, 2012 The properties of four elements \((LPFE)\) and \((UPFE)\), introduced by Isac and Persson, have been recently examined in Hilbert spaces, \(L^p\)-spaces and modular spaces. In this paper we prove a new theorem showing that a modular of form \(\rho_{\Phi}(
Bartosz Micherda
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Form Factors, Thermal States and Modular Structures [PDF]
, 1998 Form factor sequences of an integrable QFT can be defined axiomatically as solutions of a system of recursive functional equations, known as ``form factor equations''.
Babelon +36 more
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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
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Throughput Analysis for Layout Optimisation of Modular Conveyor Systems
Proceedings of the Conference on Production Systems and Logistics, 2022 In this paper, objective functions for the optimisation of modular conveyor systems will be introduced. Modular conveyor systems consist of conventional as well as modular conveyor hardware, which are arranged in form of matrix-like layouts.
Aurich, Paul +5 more
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