Related papers: p-adic Gauss integrals from the Poison summarizing…
We continue the research of Lata{\l}a on improving estimates of $p$-th moments of sums of independent random variables. We generalize some of his results in the case when $2 \leq p \leq 4$ and present a combinatorial approach for even…
The notion of determinant groupoid is a natural outgrowth of the theory of the Sato Grassmannian and thus well-known in mathematical physics. We briefly sketch here a version of the theory of determinant groupoids over an artinian local…
The Newton-Girard Formula allows one to write any elementary symmetric polynomial as a sum of products of power sum symmetric polynomials and elementary symmetric polynomials of lesser degree. It has numerous applications. We have…
Combining the derivative operator with Chu-Vandermonde convolution, we establish a class of summation formulas on generalized harmonic numbers.
We present a simple representation for analytically continued nested harmonic sums for the arbitrary complex argument. This representation can be obtained for a wide range of nested harmonic sums from a precomputed database for the pole…
In this paper, we introduce an analog of Gauss sums over function fields in positive characteristic. We establish several fundamental properties, including reflection formula, Stickelberger's theorem, and Hasse-Davenport relations. In…
The hadronic vacuum polarization contribution to the muon (g-2) value is calculated by considering a known dispersion integral which involves the $R_{e+ e-}(s)$ ratio. The theoretical part stemming from the region below 1.8 GeV is the…
In this paper we investigate congruence relationships of particular finite generalized harmonic numbers sums. We suggest more transparent and simpler method to analyse these sums and present several additional results for certain special…
In this paper, we introduce a new and efficient data augmentation approach to the posterior inference of the models with shape parameters when the reciprocal gamma function appears in full conditional densities. Our approach is to…
We describe a method for obtaining relations between higher derivative interactions in supersymmetric effective actions. The method extends to all orders in the momentum expansion. As an application, we consider the string coupling…
We describe reduced representatives for positive Rouquier complexes. These are obtained via Morse theoretical Gaussian elimination from the corresponding standard representatives. The underlying graded object is still a direct sum of…
Grand Unified Theories often involve additional Abelian group factors apart from the standard model hypercharge, that generally lead to loop-induced mixing gauge kinetic terms. In this letter, we show that at the one-loop level this effect…
In this article, we consider the estimation of exponential sums along the points of the reduction mod $p^{m}$ of a $p$-adic analytic submanifold of $ \mathbb{Z}_{p}^{n}$. More precisely, we extend Igusa's stationary phase method to this…
Standard random-effects meta-analysis relies heavily on the assumption that the underlying true effects are normally distributed. In the social sciences, where evidence synthesis increasingly involves large, highly heterogeneous datasets,…
In inverse problems, it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori assumption that the unknown can be appropriately represented…
We prove a Vasyunin-type formula for an autocorrelation function arising from a Nyman-Beurling criterion generalized to a probabilistic framework. This formula can also be seen as a reciprocity formula for cotangent sums, related to the…
The explicit formulas of operations, in particular addition and multiplication, of $p $-adic integers are presented. As applications of the results, at first the explicit formulas of operations of Witt vectors with coefficients in…
We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…
In an earlier paper we derived an analogue of the classical Voronoi summation formula for automorphic forms on GL(3), by using the theory of automorphic distributions. The purpose of the present paper is to apply this theory to derive the…
In this short note we show the equivalence of Fourier expansion and Poisson summation approaches for the series approximation of the exponential function $\exp ({-{t^2}/4})$. The application of the Poisson summation formula is shown to…