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Modular Forms and Weierstrass Mock Modular Forms
Published 2016-02-01Subjects: “…modular forms…”
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Topological modular forms
Published 2014“…From the discussion above, examples of integral modular forms of weight 4, 6, ...…”
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Mathieu moonshine and Siegel Modular Forms
Published 2021-03-01“…For some conjugacy classes, but not all, they match known modular forms. In this paper, we express the product formulae for all conjugacy classes of M 24 in terms of products of standard modular forms. …”
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4-manifolds and topological modular forms
Published 2021-05-01“…Abstract We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1, 0) theories on 4-manifolds with flavor symmetry backgrounds. …”
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Interlacing of zeros of weakly holomorphic modular forms
Published 2014-05-01“…We prove that the zeros of a family of extremal modular forms interlace, settling a question of Nozaki. …”
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THE IWASAWA MAIN CONJECTURE FOR HILBERT MODULAR FORMS
Published 2015-09-01“…Following the ideas and methods of a recent work of Skinner and Urban, we prove the one divisibility of the Iwasawa main conjecture for nearly ordinary Hilbert modular forms under certain local hypotheses. As a consequence, we prove that for a Hilbert modular form of parallel weight, trivial character, and good ordinary reduction at all primes dividing $p$, if the central critical $L$-value is zero then the $p$-adic Selmer group of it has rank at least one. …”
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MOCK THETA FUNCTIONS AND QUANTUM MODULAR FORMS
Published 2013-01-01“…Along these lines, we show that the Rogers–Fine false $\vartheta $-functions, functions which have not been well understood within the theory of modular forms, specialize to quantum modular forms.…”
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Curves on K3 surfaces and modular forms
Published 2018“…As a consequence, we prove the Katz-Klemm-Vafa conjecture evaluating λ g integrals (in all genera) in terms of explicit modular forms. Indeed, all K3 invariants in primitive classes are shown to be governed by modular forms. …”
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