Results 51 to 60 of about 378,592 (232)
Siegel modular forms of genus 2 and level 2
, 2015 We study vector-valued Siegel modular forms of genus 2 and level 2. We describe the structure of certain modules of vector-valued modular forms over rings of scalar-valued modular forms.Comment: 46 pages.
Cléry, Fabien +2 more
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Journal of Mathematical Analysis and Applications, 1974 Ramanujan's \(\tau\)-function is defined by \[ \sum_{n=1}^\infty \tau(n)x^n =x \prod_{n=1}^\infty (1 - x^n)^{24} \quad\text{ for } \vert x \vert < 1. \] The ``Ramanujan hypothesis'' is the conjecture that \(\vert \tau(n)\vert \le n^{11/2} d(n)\), where \(d(n)\) is the number of divisors of \(n\). In two earlier papers [J. Math. Anal. Appl. 30, 335--352
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On Borcherds products associated with lattices of prime discriminant
, 2003 We show that certain spaces of vector valued modular forms are isomorphic to spaces of scalar valued modular forms whose Fourier coefficients are supported on suitable progressions.
Bruinier, Jan H., Bundschuh, M.
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On the arithmetic nature of coefficients of multiplicative eta-functions
Вестник Самарского университета: Естественнонаучная серияIn the article we study the arithmetic nature of the coefficients of multiplicative eta-products, also called McKay functions. For some functions it is possible to establish Hecke correspondence between the coefficients of McKay and Hecke grossen ...
G. V. Voskresenskaya
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On quasi-modular forms, almost holomorphic modular forms, and the vector-valued modular forms of Shimura [PDF]
The Ramanujan Journal, 2014 17 pages, minor ...
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Heterotic-string amplitudes at one loop: modular graph forms and relations to open strings
Journal of High Energy Physics, 2019 We investigate one-loop four-point scattering of non-abelian gauge bosons in heterotic string theory and identify new connections with the corresponding open-string amplitude.
Jan E. Gerken +2 more
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A CLASS OF NONHOLOMORPHIC MODULAR FORMS II: EQUIVARIANT ITERATED EISENSTEIN INTEGRALS
Forum of Mathematics, Sigma, 2020 We introduce a new family of real-analytic modular forms on the upper-half plane. They are arguably the simplest class of ‘mixed’ versions of modular forms of level one and are constructed out of real and imaginary parts of iterated integrals of ...
FRANCIS BROWN
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International Journal of Number Theory, 2019 In this paper, we prove a conjecture of Broadhurst and Zudilin concerning a divisibility property of the Fourier coefficients of a meromorphic modular form using the generalization of the Shimura lift by Borcherds and Hecke operators on vector-valued modular forms developed by Bruinier and Stein.
Michael Neururer, Yingkun Li
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Journal of High Energy PhysicsWe study an approach to construct Siegel modular forms from Sp(6, Z). Zero-mode wave functions on T 6 with magnetic flux background behave Siegel modular forms at the origin.
Shota Kikuchi +4 more
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Open Mathematics, 2019 After the significant work of Zagier on the traces of singular moduli, Jeon, Kang and Kim showed that the Galois traces of real-valued class invariants given in terms of the singular values of the classical Weber functions can be identified with the ...
Eum Ick Sun, Jung Ho Yun
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