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math.LOApr 1, 2023
1
citations (OpenAlex)
authors
  • Francesco Gallinaro
  • Jonathan Kirby
institutions
  • Istituto Nazionale di Fisica Nucleare, Sezione di Pisa
  • University of East Anglia
  • University of Pisa
arXiv abstractPDF
paper

Quasiminimality of complex powers

arXiv:2304.06450 · doi:10.1017/fms.2024.82

Abstract

The complex field, equipped with the multivalued functions of raising to each complex power, is quasiminimal, proving a conjecture of Zilber and providing evidence towards his stronger conjecture that the complex exponential field is quasiminimal.

arXiv comment35 pages

References in corpus (11)

  • On Quasiminimal Excellent Classes
  • Exponential algebraicity in exponential fields
  • The theory of the exponential differential equations of semiabelian varieties
  • Quasiminimal structures and excellence
  • Pseudo-exponential maps, variants, and quasiminimality
  • A Schanuel property for exponentially transcendental powers
  • Covers of Multiplicative Groups of Algebraically Closed Fields of Arbitrary Characteristic
  • Some Definability Results in Abstract Kummer Theory
  • Finitely Presented Exponential Fields
  • Exponential Sums Equations and Tropical Geometry
  • Generic Automorphisms and Green Fields
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