Results 31 to 40 of about 609,898 (329)
Modular forms in the spectral action of Bianchi IX gravitational instantons
Journal of High Energy Physics, 2019 We prove a modularity property for the heat kernel and the Seeley-deWitt coefficients of the heat kernel expansion for the Dirac-Laplacian on the Bianchi IX gravitational instantons.
Wentao Fan +2 more
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Modular Forms on the Double Half-Plane
, 2020 We formulate a notion of modular form on the double half-plane for half-integral weights and explain its relationship to the usual notion of modular form.
Duncan, John F. R., McGady, David A.
core +1 more source
, 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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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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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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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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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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On the non-randomness of modular arithmetic progressions: a solution to a problem by V. I. Arnold [PDF]
Discrete Mathematics & Theoretical Computer Science, 2006 We solve a problem by V. I. Arnold dealing with "how random" modular arithmetic progressions can be. After making precise how Arnold proposes to measure the randomness of a modular sequence, we show that this measure of randomness takes a simplified form
Eda Cesaratto +2 more
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