Related papers: From Rolle's theorem to the Sturm-Hurwitz theorem
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
We present a simple proof of the Riemann's Hypothesis (RH) where only undergraduate mathematics is needed.
For most purposes, one can replace the use of Rolle's theorem and the mean value theorem, which are not constructively valid, by the law of bounded change. The proof of two basic results in numerical analysis, the error term for Lagrange…
We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.
This note presents a proof of P\'olya's random walk theorem using classical methods from special function theory and asymptotic analysis.
We obtain a new proof of Hurwitz's formula for the Hurwitz zeta function $\zeta(s, a)$ beginning with Hermite's formula. The aim is to reveal a nice connection between $\zeta(s, a)$ and a special case of the Lommel function $S_{\mu,…
This paper is an extension program of the notion of circle of partition developed in our first paper \cite{CoP}. As an application we prove the Erd\H{o}s-Tur\'{a}n additive base conjecture.
We give a short proof of Stein's universal multiplier theorem, purely by probabilistic methods, thus avoiding any use of harmonic analysis techniques (complex interpolation or transference methods).
We study the real counterpart of double Hurwitz numbers, called real double Hurwitz numbers here. We establish a lower bound for these numbers with respect to their dependence on the distribution of branch points. We use it to prove, under…
In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.
We reformulate, in the context of continuous logic, an oscillation theorem originally proved by G. Hjorth. We give a proof of the theorem in that setting which is similar to, but simpler than, Hjorth's original one. The point of view…
In this work we derive a functional equation in terms of the Hurwitz-Lerch zeta function along with definite integrals in terms of the incomplete gamma and Hurwitz-Lerch zeta functions. The method used in these derivations is contour…
Sturm oscillation theorem for second order differential equations was generalized to systems and higher order equations with positive leading coefficient by several authors. What we propose here is a Sturm oscillation theorem for systems of…
We show that $b$-Hurwitz numbers with a rational weight are obtained by taking an explicit limit of a Whittaker vector for the $\mathcal{W}$-algebra of type $A$. Our result is a vast generalization of several previous results that treated…
We present a simple short proof of the Fundamental Theorem of Algebra, without complex analysis and with a minimal use of topology. It can be taught in a first year calculus class.
A more detailed derivation of the Heisenberg uncertainty principle from the certainty principle is given.
We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.
We prove a conjecture of Sturmfels, Timme and Zwiernik on the ML-degrees of linear covariance models in algebraic statistics. As in our previous works on linear concentration models, the proof ultimately relies on the computation of certain…
We provide a proof of Wilson's Theorem and Wolstenholme's Theorem based on a direct approach by Lagrange requiring only basic properties of the primes and the Binomial theorem. The goal is to show how similar the two theorems are by…
We give a proof of the Marker-Steinhorn Theorem which fills a gap in previous proofs of the result.