Related papers: Decay Rates for Cusp Functions
We prove a spectral summation formula for the product of four Fourier coefficients of half-integral weight cusp forms in Kohnen's subspace. The other side of the formula involves certain generalized class numbers of pairs of quadratic forms…
In this short note, we treat an unbalanced shifted convolution sum of Fourier coefficients of cusp forms by a rather simple argument. Our result improves previous results established by more advanced approaches.
We study the behavior of the shifted convolution sum involving fourth power of the Fourier coefficients of holomorphic cusp forms with a weight function to be the $k$-full kernel function for any fixed integer $k\geq2$.
Decay processes $B\rightarrow D_{\left(s\right)}^{\left(*\right)}h$ ($h=\pi,\rho$) are studied in the framework of the confined covariant quark model using the na\"{i}ve factorization assumption. We observe that the theoretical results on…
Assuming that a function and its Fourier transform are dominated by a Gaussian, Vemuri found a sharp estimate for the decay rate of the Hermite coefficients in terms of the variance of the dominating Gaussian. Here we show that under the…
We provide a simple and new induction based treatment of the problem of distinguishing cusp forms from the growth of the Fourier coefficients of modular forms. Our approach gives the best possible ranges of the weights for this problem, and…
We consider measures supported on sets of irrational numbers possessing many consecutive partial quotients satisfying a condition based on the previous partial quotients. We show that under mild assumptions, such sets will always support…
We establish an estimate on sums of shifted products of Fourier coefficients coming from holomorphic or Maass cusp forms of arbitrary level and nebentypus. These sums are analogous to the binary additive divisor sum which has been studied…
Hadronic decays rates of the $\tau$ lepton into multi meson final states are presented. The structure of the hadronic matrix elements for various decay modes is discussed. The formalism of structure functions allows for a detailed test of…
In this article, we study the simultaneous sign changes of the Fourier coefficients of two Hilbert cusp forms of different integral weights. We also study the simultaneous non-vanishing of Fourier coefficients, of two distinct non-zero…
This article is concerned with the Fourier coefficients of cusp forms (not necessarily eigenforms) of half-integer weight lying in the plus space. We give a soft proof that there are infinitely many fundamental discriminants $D$ such that…
The ongoing and planned experimental activities with direct reference to light unflavoured pseudoscalar mesons motivate a new theoretical study regarding their properties. An overview including details on new precise calculations is…
In this paper we investigate functions that are harmonic with respect to the non-symmetric strictly $\alpha$-stable L\'evy processes on an open set $D \in \mathbb{R}^d$. We obtain the explicit formula for their boundary decay rate at parts…
Strong final-state interactions create a pronounced cusp in eta' --> eta pi0 pi0 decays. We adapt and generalize the non-relativistic effective field theory framework developed for the extraction of pi pi scattering lengths from K --> 3 pi…
A realistic estimate of the cusp effect in the eta->3pi0 decay is required for the forthcoming high precision experiments. The predictions for the size of this effect are given within the framework of nonrelativistic effective field theory.
We estimate the mean square of a short exponential sum involving Fourier coefficients of a cusp form with a linear twist, a smooth weight function, and a relatively short averaging interval.
In this paper we study the Fourier coefficients of theta functions attached to Dirichlet characters at cusps other than infinity. The method is based on expressing them in terms of explicit elements of the adelic Schwartz space and studying…
Recently we found necessary and sufficient conditions for the convergence at a preassigned point of the spherical partial sums of the Fourier integral in a class of piecewise smooth functions in Euclidean space. These yield elementary…
We study deformations of plane curve singularities from an analytic point of view and obtain some new concrete results. We show some rather unexpected properties of Puiseux coefficients treated as functions on a suitably defined parameter…
The paper studies functions defined on continuous branching lines connected into a system. A notion of spectrum degeneracy for these functions is introduced. This degeneracy is based on the properties of the Fourier transforms for processes…