Related papers: Shifted convolution sum with weighted average : $G…

We present a calculation of the twist-3 generalized parton distributions (GPDs) for gluons in the proton. Our analysis is performed within a light-front constituent model where the proton is treated as a two-body state of a spin-1 gluon and…

In this largely expository note, we explain some recent progress on new cycles on Shimura varieties and Rapoport-Zink spaces, (twisted) arithmetic fundamental lemma, and arithmetic analogs of relative Langlands program. We explain related…

The classical quadratic Gauss sum can be thought of as an exponential sum attached to a quadratic form on a cyclic group. We introduce an equivariant version of Gauss sum for arbitrary finite quadratic forms, which is an exponential sum…

In this paper we show how the GL(N) Voronoi summation formula of [MiSc2] can be rewritten to incorporate hyper-Kloosterman sums of various dimensions on both sides. This generalizes a formula for GL(4) with ordinary Kloosterman sums on both…

Learning 3D representations that generalize well to arbitrarily oriented inputs is a challenge of practical importance in applications varying from computer vision to physics and chemistry. We propose a novel multi-resolution convolutional…

We analyze certain bilinear forms involving $GL_3$ Kloosterman sums. As an application, we obtain an improved estimate for the $GL_3$ spectral large sieve inequality.

Many machine learning methods assume that the training and test data follow the same distribution. However, in the real world, this assumption is very often violated. In particular, the phenomenon that the marginal distribution of the data…

The cumulative sum (CUSUM) process is often used in change point analysis to detect changes in the mean of sequentially observed data. We provide a full description of the asymptotic distribution of $L^p, 1\leq p <\infty$, functionals of…

In this paper, we study the weighted sums of multiple t-values and of multiple t-star values at even arguments. Some general weighted sum formulas are given, where the weight coefficients are given by (symmetric) polynomials of the…

In this paper, we introduce weighted fractional generalized cumulative past entropy of a nonnegative absolutely continuous random variable with bounded support. Various properties of the proposed weighted fractional measure are studied.…

We present a fast algorithm for the total variation regularization of the $3$-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved…

Motivated by the problem of computing investment portfolio weightings we investigate various methods of clustering as alternatives to traditional mean-variance approaches. Such methods can have significant benefits from a practical point of…

We study a mean value of the shifted convolution problem over the Hecke eigenvalues of a fixed non-holomorphic cusp form. We attain a result also for a weighted case. Furthermore, we point out that the proof yields analogous upper bounds…

In a recent paper (Appl. Math. Comput. 215, 1622--1645, 2009), the authors proposed a method of summation of some slowly convergent series. The purpose of this note is to give more theoretical analysis for this transformation, including the…

We consider finite iterated generalized harmonic sums weighted by the binomial $\binom{2k}{k}$ in numerators and denominators. A large class of these functions emerges in the calculation of massive Feynman diagrams with local operator…

A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…

We prove a Burgess-like subconvex bound for twisted L-functions of a fixed irreducible cuspidal automorphic representation of GL(2) over a totally real number field. The proof is based on a spectral decomposition of shifted convolution sums…

A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.

We derive weighted sums, including binomial and double binomial sums, for the generalized Fibonacci sequence $\{G_m\}$ where for $m\ge 2$, $G_m=G_{m-1}+G_{m-2}$ with initial values $G_0$ and $G_1$.

This article describes a general method for computing automorphic forms using Voronoi-type summation formulas. It gives a numerical example where the technique is successful in quickly finding a cusp form on GL(3,Z)\GL(3,R), albeit one…