Results 1 to 10 of about 822 (88)
Ramanujan’s function k(τ)=r(τ)r2(2τ) and its modularity
Open Mathematics, 2020 We study the modularity of Ramanujan’s function k(τ)=r(τ)r2(2τ)k(\tau )=r(\tau ){r}^{2}(2\tau ), where r(τ)r(\tau ) is the Rogers-Ramanujan continued fraction.
Lee Yoonjin, Park Yoon Kyung
doaj +1 more source
A short extension of two of Spira's results [PDF]
, 2014 Two inequalities concerning the symmetry of the zeta-function and the Ramanujan $\tau$-function are improved through the use of some elementary considerations.Comment: 4 pages; to appear in J.
Trudgian, Tim
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Integrable systems and modular forms of level 2 [PDF]
, 2006 A set of nonlinear differential equations associated with the Eisenstein series of the congruent subgroup $\Gamma_0(2)$ of the modular group $SL_2(\mathbb{Z})$ is constructed. These nonlinear equations are analogues of the well known Ramanujan equations,
Ablowitz, Mark J +2 more
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Odd values of the Klein j-function and the cubic partition function [PDF]
, 2015 In this note, using entirely algebraic or elementary methods, we determine a new asymptotic lower bound for the number of odd values of one of the most important modular functions in number theory, the Klein $j$-function.
Zanello, Fabrizio
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The hexagonal versus the square lattice [PDF]
, 2002 We establish Schmutz Schaller's conjecture that the hexagonal lattice is `better' than the square lattice. Schmutz Schaller (Bulletin of the AMS 35 (1998), p.
Moree, Pieter, Riele, Herman J. J. te
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A theory of theta functions to the quintic base [PDF]
, 2013 Properties of four quintic theta functions are developed in parallel with those of the classical Jacobi null theta functions. The quintic theta functions are shown to satisfy analogues of Jacobi's quartic theta function identity and counterparts of ...
Huber, Tim
core +1 more source
The Explicit Sato-Tate Conjecture and Densities Pertaining to Lehmer-Type Questions [PDF]
, 2016 Let $f(z)=\sum_{n=1}^\infty a(n)q^n\in S^{\text{new}}_ k (\Gamma_0(N))$ be a newform with squarefree level $N$ that does not have complex multiplication.
Rouse, Jeremy, Thorner, Jesse
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Two-divisibility of the coefficients of certain weakly holomorphic modular forms
, 2011 We study a canonical basis for spaces of weakly holomorphic modular forms of weights 12, 16, 18, 20, 22, and 26 on the full modular group. We prove a relation between the Fourier coefficients of modular forms in this canonical basis and a generalized ...
A. El-Guindy +18 more
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Arithmetic properties of the Ramanujan function
, 2006 We study some arithmetic properties of the Ramanujan function $\tau(n)$, such as the largest prime divisor $P(\tau(n))$ and the number of distinct prime divisors $\omega(\tau(n))$ of $\tau(n)$ for various sequences of $n$.
Luca, Florian, Shparlinski, Igor E
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An isomorphism between the convolution product and the componentwise sum\n connected to the D'Arcais numbers and the Ramanujan tau function [PDF]
, 2020 Stefano Barbero +2 more
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