Related papers: Periodic sign changes for weakly holomorphic $\eta…

We study the form factors of the $\eta_c$ meson in the light-front quark model. We explicitly show that the transition form factor of $\eta_c \to \gamma^* \gamma$ as a function of the momentum transfer is consistent with the experimental…

In this paper, we investigate cycle integrals of weakly holomorphic modular forms. We show that these integrals coincide with the cycle integrals of classical cusp forms. We use these results to define a Shintani lift from integral weight…

We introduce the $L$-series of weakly holomorphic modular forms using Laplace transforms and give their functional equations. We then determine converse theorems for vector-valued harmonic weak Maass forms, Jacobi forms, and elliptic…

We investigate Siegel theta series for quadratic forms of signature $(m-1,1)$. On the one hand, we construct a holomorphic series that does not transform like a modular form. On the other hand, we construct a non-holomorphic series that…

In this paper, we investigate the "angular changes" behavior of some subfamilies of Fourier coefficients of both integral and half-integral weight holomorphic cusp forms, thus one gets information about signs of the real an imaginary parts…

Suppose that $\ell \geq 5$ is prime. For a positive integer $N$ with $4 \mid N$, previous works studied properties of half-integral weight modular forms on $\Gamma_0(N)$ which are supported on finitely many square classes modulo $\ell$, in…

In this paper, we consider the first negative eigenvalue of eigenforms of half-integral weight k + 1/2 and obtain an almost type bound.

In this paper we consider weakly holomorphic modular forms (i.e. those meromorphic modular forms for which poles only possibly occur at the cusps) of weight $2-k\in 2\Z$ for the full modular group $\SL_2(\Z)$. The space has a distinguished…

Let $O_L$ be the ring of integers of a number field $L$. Write $q = e^{2 \pi i z}$, and suppose that $$f(z) = \sum_{n \gg - \infty}^{\infty} a_f(n) q^n \in M_{k}^{!}(\operatorname{SL}_2(\mathbb{Z})) \cap O_L[[q]]$$ is a weakly holomorphic…

We discuss $(\pi^0,\eta,\eta')\to\gamma^*\gamma$ transition form factors using the light-front quark model. Our discussion includes the analysis of the mixing angles for $\eta-\eta'$. Our results for $Q^2…

In this thesis we discuss a rational and data-based description of the single- and double-virutal transition form factors of the lightest pseudoscalar mesons. We obtain an accurate description of these in the spacelike and low-energy…

Let $\lambda$ be an integer, and $f(z)=\sum_{n\gg-\infty} a(n)q^n$ be a weakly holomorphic modular form of weight $\lambda+\frac 12$ on $\Gamma_0(4)$ with integral coefficients. Let $\ell\geq 5$ be a prime. Assume that the constant term…

The radiative decays $\eta'(\eta)\rta\gamma\gamma$ are discussed. The modifications of the conventional PCAC formulae due to the gluonic contribution to the flavour singlet axial anomaly are given. The decay constants satisfy a modified…

Previous works have shown that certain weight $2$ newforms are $p$-adic limits of weakly holomorphic modular forms under repeated application of the $U$-operator. The proofs of these theorems originally relied on the theory of harmonic…

An eta-quotient of level $N$ is a modular form of the shape $f(z) = \prod_{\delta | N} \eta(\delta z)^{r_{\delta}}$. We study the problem of determining levels $N$ for which the graded ring of holomorphic modular forms for $\Gamma_{0}(N)$…

In this paper, we investigate sign changes of Fourier coefficients of half-integral weight cusp forms. In a fixed square class $t\mathbb{Z}^2$, we investigate the sign changes in the $tp^2$-th coefficient as $p$ runs through the split or…

We define a notion of modular forms of half-integral weight on the quaternionic exceptional groups. We prove that they have a well-behaved notion of Fourier coefficients, which are complex numbers defined up to multiplication by $\pm 1$. We…

We discuss certain features of pseudo-Hermiticity and weak pseudo-Hermiticity conditions and point out that, contrary to a recent claim, there is no inconsistency if the correct orthogonality condition is used for the class of…

In an article in the Pure and Applied Mathematics Quarterly in 2008, Duke and Jenkins investigated a certain natural basis of the space of weakly holomorphic modular forms for the full modular group $SL_2({\bf Z})$. We show here that their…

We consider some questions related to the signs of Hecke eigenvalues or Fourier coefficients of classical modular forms. One problem is to determine to what extent those signs, for suitable sets of primes, determine uniquely the modular…