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We propose a general purpose confidence interval procedure (CIP) for statistical functionals constructed using data from a stationary time series. The procedures we propose are based on derived distribution-free analogues of the $\chi^2$…
In this paper, we investigate the average behavior of ternary correlations for general $k$-divisor-bounded multiplicative functions, assuming certain second moment integral bounds for the associated $L$-functions. Our approach differs from…
We first normalize the derivative Weierstrass $\wp'$-function appearing in Weierstrass equations which give rise to analytic parametrizations of elliptic curves by the Dedekind $\eta$-function. And, by making use of this normalization of…
We propose semi-random features for nonlinear function approximation. The flexibility of semi-random feature lies between the fully adjustable units in deep learning and the random features used in kernel methods. For one hidden layer…
We study pseudorandomness and pseudorandom generators from the perspective of logical definability. Building on results from ordinary derandomization and finite model theory, we show that it is possible to deterministically construct, in…
We construct a random $n$-hypergraph for every $n$, in a given pseudofinite field.
In this paper we describe a general method to generate superoscillatory functions of several variables starting from a superoscillating sequence of one variable. Our results are based on the study of suitable infinite order differential…
This paper continues the author's previous work on a limit-free algebraic-geometric construction of the derivative in the class of polynomial functions and extends the proposed framework to elementary functions. Derivatives of rational…
We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential sums and some arithmetic problems involving points on…
Abstrct: In this note, by considering fractionally linear functions over a finite field and consequently developing an abstract sequence, we study some of its properties.
Let us consider a generalized Artin-Schreier algebraic function field extension $F$ of the rational function field $\F_{p^n}(x)$ defined over the finite field extension $K=\F_{p^n}$ of the prime field $\F_p$. We assume that $K$ is…
These lecture notes were written for a mini-course that was designed to introduce students and researchers to {\it $q$-series,} which are also called {\it basic hypergeometric series} because of the parameter $q$ that is used as a base in…
Minimal linear codes have interesting applications in secret sharing schemes and secure two-party computation. This paper uses characteristic functions of some subsets of $\mathbb{F}_q$ to construct minimal linear codes. By properties of…
We use the plethystic exponential and the Molien-Weyl formula to compute the Hilbert series (generating funtions), which count gauge invariant operators in N=1 supersymmetric SU(N_c), Sp(N_c), SO(N_c) and G_2 gauge theories with 1 adjoint…
In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques…
For a given prime $p$, a new construction of families of the complex valued sequences of period $p$ with efficient implementation is given by applying both multiplicative characters and additive characters of finite field $\mathbb{F}_p$.…
In this paper certain classes of infinite sums involving special functions are evaluated analytically by application of basic quantum mechanical principles to simple models of half harmonic oscillator and a particle trapped inside an…
For the ordered set $[n]$ of $n$ elements, we consider the class $\Bscr_n$ of bases $B$ of tropical Pl\"ucker functions on $2^{[n]}$ such that $B$ can be obtained by a series of mutations (flips) from the basis formed by the intervals in…
For a given elliptic curve $\mathbf{E}$ over a finite field of odd characteristic and a rational function $f$ on $\mathbf{E}$ we first study the linear complexity profiles of the sequences $f(nG)$, $n=1,2,\dots$ which complements earlier…
We simplify and give an alternative proof of hypoellipticity for generalizations of the singular sum of squares of complex vector fields studied by Kohn, with an appendix by Derridj and Tartakoff, in the Annals of Mathematics, vol. 162 no.…