Zobrazeno 1 - 10
of 49
pro vyhledávání: '"Mantova, Vincenzo"'
A classical tool in the study of real closed fields are the fields $K((G))$ of generalized power series (i.e., formal sums with well-ordered support) with coefficients in a field $K$ of characteristic 0 and exponents in an ordered abelian group $G$.
Externí odkaz:
http://arxiv.org/abs/2405.13815
We show that for any polynomial $F(X,Y_0,Y_1,Y_2) \in \mathbb{C}[X, Y_0, Y_1, Y_2]$, the equation $F(z,j(z),j'(z),j''(z))=0$ has a Zariski dense set of solutions in the hypersurface $F(X,Y_0,Y_1,Y_2)=0$, unless $F$ is in $\mathbb{C}[X]$ or it is divi
Externí odkaz:
http://arxiv.org/abs/2312.09974
Autor:
Mantova, Vincenzo, Masser, David
Recently Brownawell and the second author proved a "non-degenerate" case of the (unproved) "Zilber Nullstellensatz" in connexion with "Strong Exponential Closure". Here we treat some significant new cases. In particular these settle completely the pr
Externí odkaz:
http://arxiv.org/abs/2303.05592
Autor:
L'Innocente, Sonia, Mantova, Vincenzo
Publikováno v:
In Advances in Mathematics April 2024 442
Publikováno v:
International Mathematics Research Notices, Volume 2023, Issue 5, March 2023, Pages 4046-4081
Zilber's Exponential Algebraic Closedness conjecture (also known as Zilber's Nullstellensatz) gives conditions under which a complex algebraic variety should intersect the graph of the exponential map of a semiabelian variety. We prove the special ca
Externí odkaz:
http://arxiv.org/abs/2105.12679
Publikováno v:
Proc. Amer. Math. Soc. 151 (2023), 2655-2669
Inspired by Conway's surreal numbers, we study real closed fields whose value group is isomorphic to the additive reduct of the field. We call such fields omega-fields and we prove that any omega-field of bounded Hahn series with real coefficients ad
Externí odkaz:
http://arxiv.org/abs/1810.03029
Autor:
L'Innocente, Sonia, Mantova, Vincenzo
We prove that in every ring of generalised power series with non-positive real exponents and coefficients in a field of characteristic zero, every series admits a factorisation into finitely many irreducibles of infinite support, the number of which
Externí odkaz:
http://arxiv.org/abs/1710.07304
Publikováno v:
Trans. Amer. Math. Soc. 371 (2019), 3549-3592
We show that \'Ecalle's transseries and their variants (LE and EL-series) can be interpreted as functions from positive infinite surreal numbers to surreal numbers. The same holds for a much larger class of formal series, here called omega-series. Om
Externí odkaz:
http://arxiv.org/abs/1703.01995
Autor:
Mantova, Vincenzo, Matusinski, Mickaël
Publikováno v:
In "Ordered Algebraic Structures and Related Topics", 265-290, Contemp. Math., 697, Amer. Math. Soc., Providence, RI, 2017
The present article surveys surreal numbers with an informal approach, from their very first definition to their structure of universal real closed analytic and exponential field. Then we proceed to give an overview of the recent achievements on equi
Externí odkaz:
http://arxiv.org/abs/1608.03413
Autor:
L'Innocente, Sonia, Mantova, Vincenzo
Publikováno v:
Journal of Logic & Analysis 9:3 (2017) 1-16
A classical tool in the study of real closed fields are the fields $K((G))$ of generalised power series (i.e., formal sums with well-ordered support) with coefficients in a field $K$ of characteristic 0 and exponents in an ordered abelian group $G$.
Externí odkaz:
http://arxiv.org/abs/1512.04895