相关论文: Periodic sign changes for weakly holomorphic $\eta…
In this paper we study sign changes of an infinite class of $\eta$-quotients which are holomorphic modular forms. There is also a relation to Hurwitz class numbers.
In this paper, we study vanishing of Fourier coefficients of holomorphic $\eta$-quotients. We investigate examples of two different types: the first one involves integral weight CM newforms, while the second one involves half-integral…
In this paper, we investigate the sign changes of Fourier coefficients of half-integral weight Hecke eigenforms and give two quantitative results on the number of sign changes.
We establish lower bounds for (i) the numbers of positive and negative terms and (ii) the number of sign changes in the sequence of Fourier coefficients at squarefree integers of a half-integral weight modular Hecke eigenform.
In this paper, we prove some divisibility results for the Fourier coefficients of reduced modular forms of sign vectors. More precisely, we generalize a divisibility result of Siegel on constant terms when the weight is non-positive, which…
For a half integral weight modular form $f$ we study the signs of the Fourier coefficients $a(n)$. If $f$ is a Hecke eigenform of level $ N$ with real Nebentypus character, and $t$ is a fixed square-free positive integer with $a(t)\neq 0$,…
We show that signs of Fourier coefficients, on certain sub-families, determine the half-integral weight cuspidal eigenform uniquely, up to a positive constant. We also study sign change results for the product of the Fourier coefficients of…
The \eta and \eta' transition form factors in the space-like region are analyzed at low and intermediate energies in a model-independent way through the use of rational approximants. The slope and curvature parameters of the form factors as…
We examine the Fourier coefficients of modular forms in a canonical basis for the spaces of weakly holomorphic modular forms of weights 4, 6, 8, 10, and 14, and show that these coefficients are often highly divisible by the primes 2, 3, and…
We attempt to compute expressions in terms of the Dedekind eta function for all weight 2 new cusp forms with level up to 100, using methods of Allen et. al. In cases where no expression exists, we raise the level instead of the weight,…
In this short note, we aim to prove that the Fourier coefficients of the modular function $ \frac{\eta^{24}(\tau)}{\eta^{24}(2\tau)} $ possess a sign-change property.
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.…
In this paper, we study the transition form factors of the lightest pseudoscalar mesons, $\pi^0$, $\eta$, and $\eta'$, within the framework of resonance chiral theory. Our analysis is performed based on the data of time-like and space-like…
We establish an Eichler-Shimura isomorphism for weakly modular forms of level one. We do this by relating weakly modular forms with rational Fourier coefficients to the algebraic de Rham cohomology of the modular curve with twisted…
In this note, we describe several new examples of holomorphic modular forms on the group SU(2,1). These forms are distinguished by having weight $\frac{1}{3}$. We also describe a method for determining the levels at which one should expect…
The $\eta$ transition form factor is analysed for the first time in both space- and time-like regions at low and intermediate energies in a model-independent approach through the use of rational approximants. The $\eta\rightarrow…
In this paper we investigate the Fourier coefficients of harmonic Maass forms of negative half-integral weight. We relate the algebraicity of these coefficients to the algebraicity of the coefficients of certain canonical meromorphic…
The electromagnetic transition form factors of $\eta$ and $\eta'$ are calculated in the light-cone perturbation theory. We show that it is unreliable to determine the \eta-\etap'$ mixing angle without any additional normalization conditions…
The $\pi^0$, $\eta$, and $\eta^\prime$ transition form factors in the space-like region are analyzed at low and intermediate energies in a model-independent way through the use of rational approximants. Slope and curvature parameters as…
It has been realized for a long time that knowing the \eta and \eta' wave functions in terms of quark and gluon components probes our understanding of non-perturbative QCD dynamics. Great effort has been given to this challenge -- yet no…