Related papers: On the Lojasiewicz exponent at infinity for polyno…
We extend to several variables an earlier result of ours, according to which an entire function of one variable of sufficiently small exponential type, having all derivatives of even order taking integer values at two points, is a…
We provide algorithms for the absolute and alternating Ostrowski Expansions of the continuum and provide proofs for their uniqueness.
In this article we study polynomial logarithmic $q$-forms on a projective space and characterize those that define singular foliations of codimension $q$. Our main result is the algebraic proof of their infinitesimal stability when $q=2$…
We apply methods from Malliavin calculus to prove an infinite-dimensional version of Hormander's theorem for stochastic evolution equations in the spirit of Da Prato-Zabczyk. This result is used to show that HJM-equations from interest rate…
We present a theorem on taking the repeated indefinite summation of a holomorphic function $\phi(z)$ in a vertical strip of $\mathbb{C}$ satisfying exponential bounds as the imaginary part grows. We arrive at this result using transforms…
The Kurdyka-{\L}ojasiewicz (K{\L}) property, exponent and modulus have played a very important role in the study of global convergence and rate of convergence for optimal algorithms. In this paper, at a stationary point of a locally lower…
The true complexity of a polynomial progression in finite fields corresponds to the smallest-degree Gowers norm that controls the counting operator of the progression over finite fields of large characteristic. We give a conjecture that…
We find a wide class of Levy-Loewner evolutions for which the value of integral means beta-spectrum $\beta(q)$ at $q=2$ is the maximal real eigenvalue of a three-diagonal matrix. The second moments of derivatives of corresponding conformal…
We initiate the study of the coefficients of the distinct monomials in the expansion of the multivariate polynomials $x_1(x_1+x_2)\cdots(x_1+x_2+\cdots+x_n), n\in\N$. In particular we obtain several results regarding their maximal…
We give formulas for the number of polynomials over a finite field with given root multiplicities, in particular in cases when the formula is surprisingly simple (a power of q). Besides this concrete interpretation, we also prove an…
A two-variable generalization of the Big $-1$ Jacobi polynomials is introduced and characterized. These bivariate polynomials are constructed as a coupled product of two univariate Big $-1$ Jacobi polynomials. Their orthogonality measure is…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
Inspired by Armin Straub's conjecture (arXiv:1601.07161) about the number and maximal size of (2n+1, 2n+3)-core partitions with distinct parts, we develop relatively efficient, symbolic-computational algorithms, based on non-linear…
This paper describes a novel method to approximate the polynomial coefficients of regression functions, with particular interest on multi-dimensional classification. The derivation is simple, and offers a fast, robust classification…
We examine the asymptotic expansion of the Touchard polynomials $T_n(z)$ (also known as the exponential polynomials) for large $n$ and complex values of the variable $z$. In our treatment $|z|$ may be finite or allowed to be large like…
Given a finite field $\F_q$ and $n\in \N^*$, one could try to compute all polynomial endomorphisms $\F_q^n\lp \F_q^n$ up to a certain degree with a specific property. We consider the case $n=3$. If the degree is low (like 2,3, or 4) and the…
We consider incomplete exponential sums in several variables of the form S(f,n,m) = \frac{1}{2^n} \sum_{x_1 \in \{-1,1\}} ... \sum_{x_n \in \{-1,1\}} x_1 ... x_n e^{2\pi i f(x)/p}, where m>1 is odd and f is a polynomial of degree d with…
We show an explicit formula relating \'etale polylogarithms introduced by Wojtkowiak and finite polylogarithms introduced by Elbaz-Vincent and Gangl. This formula is an \'etale analog of Besser's formula relating Coleman's $p$-adic…
Let $\mathbb F_q$ be the finite field with $q$ elements, $f, g\in \mathbb F_q[x]$ be polynomials of degree at least one. This paper deals with the asymptotic growth of certain arithmetic functions associated to the factorization of the…
We study the growth of polynomials on semialgebraic sets. For this purpose we associate a graded algebra to the set, and address all kinds of questions about finite generation. We show that for a certain class of sets, the algebra is…