Results 21 to 30 of about 359 (68)
A generating function of the squares of Legendre polynomials
, 2012 We relate a one-parametric generating function for the squares of Legendre polynomials to an arithmetic hypergeometric series whose parametrisation by a level 7 modular function was recently given by Shaun Cooper. By using this modular parametrisation we
Zudilin, Wadim
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On the zeros of weakly holomorphic modular forms
, 2014 In this article, we study the nature of zeros of weakly holomorphic modular forms. In particular, we prove results about transcendental zeros of modular forms of higher levels and for certain Fricke groups which extend a work of Kohnen.
Gun, Sanoli, Saha, Biswajyoti
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Equidistribution of signs for Hilbert modular forms of half-integral weight
, 2018 We prove an equidistribution of signs for the Fourier coefficients of Hilbert modular forms of half-integral weight. Our study focuses on certain subfamilies of coefficients that are accessible via the Shimura correspondence.
Kaushik, Surjeet +2 more
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Primitive and totally primitive Fricke families with applications
, 2016 We introduce the primitivity of Fricke families, and give some examples. As its application, we first construct generators of the function field of the modular curve of level $N$ in terms of Fricke functions and Siegel functions, respectively ...
Jung, Ho Yun +2 more
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Recurrence relations satisfied by some arithmetic groups
Open MathematicsRecently, recurrence relations satisfied by the modular traces of the Hauptmodul for Γ0(N){\Gamma }_{0}\left(N) of genus zero have been established. However, these relations do not determine all values of the modular traces.
Kang Hee Doo +2 more
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On a relation between certain $q$-hypergeometric series and Maass waveforms
, 2016 In this paper, we answer a question of Li, Ngo, and Rhoades concerning a set of $q$-series related to the $q$-hypergeometric series $\sigma$ from Ramanajun's lost notebook.
Krauel, Matthew +2 more
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Differential equations for septic theta functions
, 2013 We demonstrate that quotients of septic theta functions appearing in S. Ramanujan's Notebooks and in F. Klein's work satisfy a new coupled system of nonlinear differential equations with interesting symmetric form.
Huber, Tim, Lara, Danny
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On the ramification of modular parametrizations at the cusps
, 2018 We investigate the ramification of modular parametrizations of elliptic curves over Q at the cusps. We prove that if the modular form associated to the elliptic curve has minimal level among its twists by Dirichlet characters, then the modular ...
Brunault, François
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An elementary approach to toy models for D. H. Lehmer's conjecture
, 2010 In 1947, Lehmer conjectured that the Ramanujan's tau function $\tau (m)$ never vanishes for all positive integers $m$, where $\tau (m)$ is the $m$-th Fourier coefficient of the cusp form $\Delta_{24}$ of weight 12.
B. B. Venkov +8 more
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Equations of Bielliptic Modular Curves [PDF]
, 2012 We give a procedure to determine equations for the modular curves $X_0(N)$ which are bielliptic and equations for the 30 values of $N$ such that $X_0(N)$ is bielliptic and nonhyperelliptic are ...
González, Josep
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