Related papers: Errata, updates of the references, etc., for the b…
In this article, we provide an application of hypergeometric evaluation identities, including a strange valuation of Gosper, to prove several supercongruences related to special valuations of truncated hypergeometric series. In particular,…
We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…
These condensed notes treat some basic notions in Tropical Geometry (varieties, cycles, modifications, equivalence). These topics are to be extended, illustrated and included to the upcoming book project…
A quick overview is provided on the current development of the WP metric geometry.
Explicit expressions for the hypergeometric series ${}_2F_1(-n, a; 2a\pm j;2)$ and ${}_2F_1(-n, a; -2n\pm j;2)$ for positive integer $n$ and arbitrary integer $j$ are obtained with the help of generalizations of Kummer's second and third…
We correct some tables and figures in [A.P. Bustamante and R.C. Calleja, Physica D: Nonlinear Phenomena, 395 (2019), pp. 15-23, arXiv:1712.05476]. We also report on the new computations that verify the accuracy of the data and extend the…
Comment on "Liquids on Topologically Nanopatterned Surfaces" by O. Gang et al, Phys. Rev. Lett. 95, 217801 (2005). See also an erratum published by O. Gang et al (Phys Rev Lett, to appear)
We make two tiny corrections to our previous paper with the same title, and also obtain, as a bonus, something new.
Existing statistical learning guarantees for general kernel regressors often yield loose bounds when used with finite-rank kernels. Yet, finite-rank kernels naturally appear in several machine learning problems, e.g.\ when fine-tuning a…
The most critical component of any adaptive numerical quadrature routine is the estimation of the integration error. Since the publication of the first algorithms in the 1960s, many error estimation schemes have been presented, evaluated…
We show that several terminating summation and transformation formulas for basic hypergeometric series can be proved in a straightforward way. Along the same line, new finite forms of Jacobi's triple product identity and Watson's quintuple…
This is the 3rd version with major updates and revisions to the 2nd version of the same title. In this article we have collected and corrected some common mistakes made by Chinese students in writing astronomy and physics literature in…
This paper describes the analysis of Lagrange interpolation errors on tetrahedrons. In many textbooks, the error analysis of Lagrange interpolation is conducted under geometric assumptions such as shape regularity or the (generalized)…
We prove some new semi-finite forms of bilateral basic hypergeometric series. One of them yields in a direct limit Bailey's celebrated ${}_6\psi_6$ summation formula, answering a question recently raised by Chen and Fu ({\em Semi-Finite…
In 2010, Kh. Hessami Pilehrood and T. Hessami Pilehrood introduced generating function identities used to obtain series accelerations for values of Dirichlet's $\beta$ function, via the Markov--Wilf--Zeilberger method. Inspired by these…
In this brief note, we show how to apply Kummer's and other quadratic transformation formulas for Gauss' and generalized hypergeometric functions in order to obtain transformation and summation formulas for series with harmonic numbers that…
This note completes a talk given at the conference Curves over Finite Fields: past, present and future celebrating the publication the book {\em Rational Points on Curves over Finite Fields by J.-P. Serre and organised at Centro de ciencias…
This expository piece expounds on major themes and clarifies technical details of the paper "Kaufman and Falconer estimates for radial projections and a continuum version of Beck's theorem" of Orponen, Shmerkin, and Wang.
In terms of the analytic continuation method, we prove three transformation formulas involving bilateral basic hypergeometric series. One of them is equivalent to Jouhet's result involving two $_8\psi_8$ series and two $_8\phi_7$ series.
The last decade has seen the emergence of a wide range of automated calculations for supersymmetric extensions of the Standard Model. This guide contains a brief summary of these, with the main focus on hadron collider phenomenology, as…