Add to ORKGABSTRACT. The paper answers an old question of Pólya involving Descartes ’ Rule of Signs and a related conjecture of Karlin involving the signs of Wronskians of entire functions and their derivatives. Counterexamples are given along with classes of functions for which the conjecture is valid. 0. Introduction. The purpose of this paper is to answer an old unsolved question of Pólya (c. 1934) and to resolve a related conjecture of Karlin (c. 1967). In Section 1 we state Pólya’s question, Karlin’s conjecture, provide some background information and recall the defi-nitions and terminology that will be used in the sequel. For a genera
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The main objective of this text is the study of the Descartes' rule of signs and the generalized Des...
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International audienceWe discuss how one could study asymptotics of cyclotomic quantities via the me...
We generalize Waldschmidt's bound for Leopoldt's defect and prove a similar bound for Gross's defect...
Since Hooley's seminal 1967 resolution of Artin's primitive root conjecture under the Generalized Ri...
Abstract. Motivated by the recent solution of Karlin’s conjecture, properties of functions in the La...
Motivated by the recent solution of Karlin's conjecture, properties of functions in the Laguerre-Pol...
It may seem a funny notion to write about theorems as old and rehashed as Descartes’s rule of signs,...
Abstract. In this paper, we study the question that an entire function f(z) and its k-th derivative ...
Descartes ’ Rule of Signs states that the number of positive roots of a polynomial p(x) with real co...
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, includ...
The main objective of this text is the study of the Descartes' rule of signs and the generalized Des...
integer a # * 1, or a perfect square, there exist infinitely many primes p for which a is a primiti...
As a special case of a well-known conjecture of Artin, it is expected that a system of R additive fo...
We dedicate this article to the memory of Philippe Flajolet Abstract. This paper studies the coeffic...
Abstract. In, 1984, Helga Schirmer proved that one direction of arkovskn's Theorem holds for al...
This article is concerned with classifying the provably total set-functions of Kripke-Platek set the...
International audienceWe discuss how one could study asymptotics of cyclotomic quantities via the me...
We generalize Waldschmidt's bound for Leopoldt's defect and prove a similar bound for Gross's defect...
Since Hooley's seminal 1967 resolution of Artin's primitive root conjecture under the Generalized Ri...