Results 11 to 20 of about 346 (52)
Torus knots and quantum modular forms [PDF]
Research in the Mathematical Sciences, 2014 In this paper we compute a q-hypergeometric expression for the cyclotomic expansion of the colored Jones polynomial for the left-handed torus knot (2,2t+1). We use this to define a family of q-series, the simplest case of which is the generating function
K. Hikami, Jeremy Lovejoy
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Weierstrass mock modular forms and elliptic curves [PDF]
Research in Number Theory, 2014 Mock modular forms, which give the theoretical framework for Ramanujan’s enigmatic mock theta functions, play many roles in mathematics. We study their role in the context of modular parameterizations of elliptic curves E/Q$E/\mathbb {Q}$.
Claudia Alfes +3 more
semanticscholar +2 more sources
Mock modular forms and class number relations [PDF]
Research in the Mathematical Sciences, 2013 PurposeAlmost 40 years ago, H. Cohen formulated a conjecture about the modularity of a certain infinite family of functions involving the generating function of the Hurwitz class numbers of binary quadratic forms.MethodsWe use techniques from the theory ...
Michael H. Mertens
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Negative index Jacobi forms and quantum modular forms [PDF]
Research in the Mathematical Sciences, 2014 In this paper, we consider the Fourier coefficients of a special class of meromorphic Jacobi forms of negative index considered by Kac and Wakimoto. Much recent work has been done on such coefficients in the case of Jacobi forms of positive index, but ...
K. Bringmann, T. Creutzig, Larry Rolen
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Central L‐values of elliptic curves and local polynomials
Proceedings of the London Mathematical Society, Volume 120, Issue 5, Page 742-769, May 2020., 2020 Abstract Here we study the recently introduced notion of a locally harmonic Maass form and its applications to the theory of L‐functions. In particular, we find a criterion for vanishing of certain twisted central L‐values of a family of elliptic curves, whereby vanishing occurs precisely when the values of two finite sums over canonical binary ...
Stephan Ehlen +3 more
wiley +1 more source
Traces of Singular Values and Borcherds Products [PDF]
, 2003 Let p be a prime for which the congruence group Γ0(p)* is of genus zero, and let jp* be the corresponding Hauptmodul. Let f be a nearly holomorphic modular form of weight 1/2 on Γ0(4p) which satisfies some congruence condition on its Fourier coefficients.
Chang-Heon Kim
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Note on the problem of Ramanujan’s radial limits
Advances in Differential Equations, 2014 Ramanujan in his deathbed letter to GH Hardy concerned the asymptotic properties of modular forms and mock theta functions. For the mock theta function f(q), he claimed that as q approaches an even order 2k root of unity ζ, limq→ζ(f(q)−(−1)k(1−q)(1−q3 ...
Bin Chen, Haigang Zhou
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Bounds for twisted symmetric square L-functions via half-integral weight periods
Forum of Mathematics, Sigma, 2020 We establish the first moment bound $$\begin{align*}\sum_{\varphi} L(\varphi \otimes \varphi \otimes \Psi, \tfrac{1}{2}) \ll_\varepsilon p^{5/4+\varepsilon} \end{align*}$$ for triple product L-functions, where $\Psi $ is a fixed Hecke ...
Paul D. Nelson
doaj +1 more source
Umbral moonshine and the Niemeier lattices [PDF]
Research in the Mathematical Sciences, 2013 In this paper, we relate umbral moonshine to the Niemeier lattices - the 23 even unimodular positive-definite lattices of rank 24 with non-trivial root systems.
Miranda CN Cheng +2 more
semanticscholar +1 more source
Research in the Mathematical Sciences, 2014 Monstrous moonshine relates distinguished modular functions to the representation theory of the Monster . The celebrated observations that 1=1,196884=1+196883,21493760=1+196883+21296876,……(*)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage ...
J. Duncan, Michael J. Griffin, K. Ono
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