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pro vyhledávání: '"Waldschmidt, Michel"'
Autor:
Fouvry, Étienne, Waldschmidt, Michel
We consider some families of binary binomial forms $aX^d+bY^d$, with $a$ and $b$ integers. Under suitable assumptions, we prove that every rational integer $m$ with $|m|\ge 2$ is only represented by a finite number of the forms of this family (with v
Externí odkaz:
http://arxiv.org/abs/2306.02462
Autor:
Waldschmidt, Michel
Publikováno v:
Proceedings of the 87th Annual Conference of the Indian Mathematical Society, December 2021. The Mathematics Student, Volume 91 (Nos. 1-2), 2022, 79-95
According to Lidstone interpolation theory, an entire function of exponential type $<\pi$ is determined by it derivatives of even order at $0$ and $1$. This theory can be generalized to several variables. Here we survey the theory for a single variab
Externí odkaz:
http://arxiv.org/abs/2303.04514
Autor:
Fouvry, Étienne, Waldschmidt, Michel
We extend our previous results on the number of integers which are values of some cyclotomic form of degree larger than a given value (see \cite{FW1}), to more general families of binary forms with integer coefficients. Our main ingredient is an asym
Externí odkaz:
http://arxiv.org/abs/2206.03733
Autor:
Waldschmidt, Michel
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 polynomial. The pro
Externí odkaz:
http://arxiv.org/abs/2112.02529
Publikováno v:
Computational Complexity, Vol.32, (2023), Article 1
We present a uniform description of sets of $m$ linear forms in $n$ variables over the field of rational numbers whose computation requires $m(n - 1)$ additions.
Externí odkaz:
http://arxiv.org/abs/2110.04657
Autor:
Waldschmidt, Michel
An integer--valued function is an entire function which maps the nonnegative integers $\mathbb N$ to the integers. An example is $2^z$. A Hurwitz function is an entire function having all derivatives taking integer values at $0$. An example is ${\mat
Externí odkaz:
http://arxiv.org/abs/2002.01223
Autor:
Waldschmidt, Michel
Given a subset $S=\{s_0, s_1\}$ of the complex plane with two points and an infinite subset ${\mathscr S}$ of $S\times {\mathbb N}$, where ${\mathbb N}=\{0,1,2,\dots\}$ is the set of nonnegative integers, we ask for a lower bound for the order of gro
Externí odkaz:
http://arxiv.org/abs/1912.00173
Autor:
Waldschmidt, Michel
Publikováno v:
Moscow J. Comb. Number Th. 9 (2020) 371-388
Let $s_0,s_1,\dots,s_{m-1}$ be complex numbers and $r_0,\dots,r_{m-1}$ rational integers in the range $0\le r_j\le m-1$. Our first goal is to prove that if an entire function $f$ of sufficiently small exponential type satisfies $f^{(mn+r_j)}(s_j)\in{
Externí odkaz:
http://arxiv.org/abs/1912.00174
Autor:
Fouvry, Etienne, Waldschmidt, Michel
For each integer $d\ge 4$, we study the sequence of positive integers which are represented by one at least of the cyclotomic binary forms $\Phi_n(X,Y)$, with $n$ a positive integer satisfying $\varphi(n)\ge d$. The case $d=2$ was studied in our prev
Externí odkaz:
http://arxiv.org/abs/1909.01892
Autor:
Levesque, Claude, Waldschmidt, Michel
Publikováno v:
South Pacific Journal of Pure & Applied Mathematics, vol. 2, No 3 (2015), 65-83
Let $ \prod_{i=1}^d (X-\alpha_i Y) \in{\mathbb C}[X,Y]$ be a binary form and let $\epsilon_1,\dots,\epsilon_d$ be nonzero complex numbers. We consider the family of binary forms $ \prod_{i=1}^d (X-\alpha_i \epsilon_i^aY)$, $a\in {\mathbb Z}$, which w
Externí odkaz:
http://arxiv.org/abs/1802.05154