Results 21 to 30 of about 334 (46)
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
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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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
core +1 more source
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
doaj +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
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 +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
, 2019 For an elliptic curve $E$ over $K$, the Birch and Swinnerton-Dyer conjecture predicts that the rank of Mordell-Weil group $E(K)$ is equal to the order of the zero of $L(E_{/ K},s)$ at $s=1$.
Morita, Kazuma
core
On non-vanishing and sign changes of the Fourier coefficients of Hilbert cusp forms
, 2017 In this article, we study (simultaneous) non-vanishing, (simultaneous) sign changes of Fourier coefficients of (two) Hilbert cusp forms ...
Dalal, Tarun, Kumar, Narasimha
core