Zobrazeno 1 - 10
of 258
pro vyhledávání: '"van Der Hoeven, Joris"'
We show that all maximal Hardy fields are elementarily equivalent as differential fields to the differential field $\mathbb T$ of transseries, and give various applications of this result and its proof.
Comment: 80 pp; extracted for publication
Comment: 80 pp; extracted for publication
Externí odkaz:
http://arxiv.org/abs/2408.05232
We show that every Hardy field extends to an $\omega$-free Hardy field. This result relates to classical oscillation criteria for second-order homogeneous linear differential equations. It is essential in [12], and here we apply it to answer question
Externí odkaz:
http://arxiv.org/abs/2404.03695
We define the universal exponential extension of an algebraically closed differential field and investigate its properties in the presence of a nice valuation and in connection with linear differential equations. Next we prove normalization theorems
Externí odkaz:
http://arxiv.org/abs/2403.19732
Consider a sparse multivariate polynomial f with integer coefficients. Assume that f is represented as a "modular black box polynomial", e.g. via an algorithm to evaluate f at arbitrary integer points, modulo arbitrary positive integers. The problem
Externí odkaz:
http://arxiv.org/abs/2312.17664
Consider a sparse polynomial in several variables given explicitly as a sum of non-zero terms with coefficients in an effective field. In this paper, we present several algorithms for factoring such polynomials and related tasks (such as gcd computat
Externí odkaz:
http://arxiv.org/abs/2312.17380
Surreal numbers form the ultimate extension of the field of real numbers with infinitely large and small quantities and in particular with all ordinal numbers. Hyperseries can be regarded as the ultimate formal device for representing regular growth
Externí odkaz:
http://arxiv.org/abs/2310.14879
For any ordinal $\alpha > 0$, we show how to define a hyperexponential $E_{\omega^{\alpha}}$ and a hyperlogarithm $L_{\omega^{\alpha}}$ on the class $\mathbf{No}^{>, \succ}$ of positive infinitely large surreal numbers. Such functions are archetypes
Externí odkaz:
http://arxiv.org/abs/2310.14873
We show how to fill "countable" gaps in Hardy fields. We use this to prove that any two maximal Hardy fields are back-and-forth equivalent.
Comment: 58 pp; revised based on comments by a referee
Comment: 58 pp; revised based on comments by a referee
Externí odkaz:
http://arxiv.org/abs/2308.02446
Conway's field No of surreal numbers comes both with a natural total order and an additional "simplicity relation" which is also a partial order. Considering No as a doubly ordered structure for these two orderings, an isomorphic copy of No into itse
Externí odkaz:
http://arxiv.org/abs/2305.02001
We show that all maximal Hardy fields are elementarily equivalent as differential fields, and give various applications of this result and its proof. We also answer some questions on Hardy fields posed by Boshernitzan.
Comment: 471 pp. This docu
Comment: 471 pp. This docu
Externí odkaz:
http://arxiv.org/abs/2304.10846