10 citations · 10 across the 3 of their papers we have counts for
8 papers
Irreducibility in generalized power series
Antongiulio Fornasiero, Noa Lavi, Sonia L'Innocente +1
A classical tool in the study of real closed fields are the fields of generalized power series (i.e., formal sums with well-ordered support) with coefficients in a field $…
Polynomial-exponential equations -- some new cases of solvability
Vincenzo Mantova, David Masser
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 so…
A geometric approach to some systems of exponential equations
Vahagn Aslanyan, Jonathan Kirby, Vincenzo Mantova
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…
Exponential fields and Conway's omega-map
Alessandro Berarducci, Salma Kuhlmann, Vincenzo Mantova +1
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…
A factorisation theory for generalised power series and omnific integers
Sonia L'Innocente, Vincenzo Mantova
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 int…
Transseries as germs of surreal functions
Alessandro Berarducci, Vincenzo Mantova
We show that Écalle'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 fo…