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Difference between Learning Basic Form Generation and Automotive Exterior Design
Education Sciences, 2019 This study explores the correlation between learning about basic form factors and learning automotive exterior design (AED) for the first time. To help beginner AED students learn smoothly, we developed modular courses and proposed to teach basic form ...
Shih-Hung Cheng +2 more
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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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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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Arithmetic of generalized Dedekind sums and their modularity
Open Mathematics, 2018 Dedekind sums were introduced by Dedekind to study the transformation properties of Dedekind η function under the action of SL2(ℤ). In this paper, we study properties of generalized Dedekind sums si,j(p, q). We prove an asymptotic expansion of a function
Choi Dohoon +3 more
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Modular Forms and Weierstrass Mock Modular Forms
Mathematics, 2016 Alfes, Griffin, Ono, and Rolen have shown that the harmonic Maass forms arising from Weierstrass ζ-functions associated to modular elliptic curves “encode” the vanishing and nonvanishing for central values and derivatives of twisted Hasse-Weil L ...
Amanda Clemm
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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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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.
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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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