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

Using the circle method, we obtain subconvex bounds for GL(3) L-functions twisted by a character modulo a prime p, hybrid in the t and p-aspects.

We compute the sum and the alternating sum of the reciprocals of triangular numbers using two standard methods from calculus: a telescoping series approach and a power series approach. We then extend these results to generalized…

We give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. For proper \'etale groupoids, Tu and Xu provide a map between the periodic cyclic cohomology of a gerbe-twisted…

Using the Kuznetsov trace formula, we prove a spectral decomposition for the sums of generalized Dirichlet $L$-functions. Among applications are an explicit formula relating norms of prime geodesics to moments of symmetric square…

In \cite{CGPWW2021}, it was conjectured that a particular shifted sum of even divisor sums vanishes, and in \cite{SDK}, a formal argument was given for this vanishing. Shifted convolution sums of this form appear when computing the Fourier…

We study the shifted convolution sums associated to completely multiplicative functions taking values in $\{\pm 1\}$ and give combinatorical proofs of two recent results in the direction of Chowla's conjecture. We also determine the…

Inversion theorems of Wiener type are essential tools in analysis and number theory. We derive a weighted version of an inversion theorem of Wiener type for general Dirichlet series from that of Edwards from 1957, and we outline an…

Let $f$ be a cuspidal newform (holomorphic or Maass) of arbitrary level and nebentypus and denote by $\lambda_f(n)$ its $n$-th Hecke eigenvalue. Let $$ r(n)=\#\left\{(n_1,n_2)\in \mathbb{Z}^2:n_1^2+n_2^2=n\right\}. $$ In this paper, we…

The paper contains the inversion formula for the weighted spherical mean. The interest to reconstruction a function by its integral by sphere grews tremendously in the last six decades, stimulated by the spectrum of new problems and methods…

This is a sequel to our previous articles \cite{Kw23, Kw23a+}. In this work, we apply recent techniques that fall under the banner of `Period Reciprocity' to study moments of $GL(3)\times GL(2)$ $L$-functions in the non-archimedean aspects,…

The mean shift algorithm is a popular way to find modes of some probability density functions taking a specific kernel-based shape, used for clustering or visual tracking. Since its introduction, it underwent several practical improvements…

First we generalize a famous lemma of Gallagher on the mean square estimate for exponential sums by plugging a weight in the right hand side of Gallagher's original inequality. Then we apply it in the special case of the Cesaro weight, in…

We compute an asymptotic formula for the twisted moment of GL(3)xGL(2) L-functions and their derivatives. As an application we prove that symmetric-square lifts of GL(2) Maass forms are uniquely determined by the central values of the…

We recapitulate the method which resums the truncated perturbation series of a physical observable in a way which takes into account the structure of the leading infrared renormalon. We apply the method to the Gross-Llewellyn Smith (GLS)…

While several instances of shifted convolution problems for GL(3) x GL(2) have been solved, the case where one factor is the classical divisor function and one factor is a GL(3) Fourier coefficient has remained open. We solve this case in…

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 prove an asymptotic formula for the smoothed shifted convolution of the generalised divisor function $d_k(n)$ and the divisor function $d(n)$, with a power-saving error term independent of $k$. In particular, when $k$ is large, this is…

This paper generalises the exponential family GLM to allow arbitrary distributions for the response variable. This is achieved by combining the model-assisted regression approach from survey sampling with the GLM scoring algorithm, weighted…

This paper studies a family of convolution quadratures, a numerical technique for efficient evaluation of convolution integrals. We employ the block generalized Adams method to discretize the underlying initial value problem, departing from…

The performance of neural networks has been significantly improved by increasing the number of channels in convolutional layers. However, this increase in performance comes with a higher computational cost, resulting in numerous studies…