Results 21 to 30 of about 342 (48)

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, Koo, Ja Kyung, Shin, Dong Hwa   +2 more
core   +1 more source

Rigid realizations of modular forms in Calabi--Yau threefolds

, 2017
We construct examples of modular rigid Calabi--Yau threefolds, which give a realization of some new weight 4 cusp ...
Burek, Dominik
core   +1 more source

Recurrence relations satisfied by some arithmetic groups

Open Mathematics
Recently, 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, Kim Chang Heon, Min Kyeong Seok   +2 more
doaj   +1 more source

Modular Invariant of Quantum Tori II: The Golden Mean [PDF]

, 2012
In our first article in this series ("Modular Invariant of Quantum Tori I: Definitions Nonstandard and Standard" arXiv:0909.0143) a modular invariant of quantum tori was defined.
Bernard, C. Castaño, Gendron, T. M.
core  

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
core   +1 more source

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, B. B. Venkov, D. A. Cox, D. B. Zagier, E. Bannai, Eiichi Bannai, P. de la Harpe, Tsuyoshi Miezaki, Vladimir A Yudin   +8 more
core   +1 more source

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
core   +1 more source

On the Mahler measure of $1+X+1/X+Y+1/Y$

, 2011
We prove a conjectured formula relating the Mahler measure of the Laurent polynomial $1+X+X^{-1}+Y+Y^{-1}$, to the $L$-series of a conductor 15 elliptic curve.Comment: 18 pages, Fixed typos in Lemmas 3 and
Berndt, Bertin, Borwein, Borwein, Boyd, Boyd, Boyd, Brunault, Deninger, Guillera, Kurokawa, Köhler, Lalí, Martin, Mathew Rogers, Mellit, Pathakjee, Rodriguez-Villegas, Rogers, Rogers, Rolfsen, Smyth, Wadim Zudilin   +22 more
core   +3 more sources

Zeros of weakly holomorphic modular forms of levels 2 and 3

, 2013
Let $M_k^\sharp(N)$ be the space of weakly holomorphic modular forms for $\Gamma_0(N)$ that are holomorphic at all cusps except possibly at $\infty$. We study a canonical basis for $M_k^\sharp(2)$ and $M_k^\sharp(3)$ and prove that almost all modular ...
Garthwaite, Sharon Anne, Jenkins, Paul
core   +1 more source

On the infinite Borwein product raised to a positive real power. [PDF]

Ramanujan J, 2023
Schlosser MJ, Zhou NH.
europepmc   +1 more source