Relevant Background
Relevant Background
It would be impossible to give an exhaustive list of all the relevant literature (that would amount to almost all of maths), but below I give a list of articles that, for various reasons, I keep going back to.
A remark on Zilber's pseudo-exponentiation, Dave Marker
J. Symbolic Logic 2006
Polynomial exponential equations and Zilber's conjecture, Vincenzo Mantova (with an appendix by Vincenzo Mantova and Umberto Zannier)
Bull. Lond. Math. Soc. 2016
Zero estimates with moving targets, W. D. Brownawell and David Masser
J. Lond. Math. Soc. 2017
Generic solutions of equations with iterated exponentials, Paola D'Aquino, Antongiulio Fornasiero and Giuseppina Terzo
Trans. Amer. Math. Soc. 2018
Blurred complex exponentiation, Jonathan Kirby
Selecta Math. 2019
A weak version of the strong exponential closure, Paola D'Aquino, Antongiulio Fornasiero and Giuseppina Terzo
Israel J. Math. 2021
Exponential sum equations and tropical geometry, Francesco Gallinaro
Selecta Math. (N.S.) 2023
Polynomial exponential equations — some new cases of solvability, Vincenzo Mantova and David Masser
Proc. London Math. Soc. 2024
Quasiminimality of complex powers, Francesco Gallinaro and Jonathan Kirby
Forum of Math. Sigma 2024
Solving systems of equations of raising-to-powers type, Francesco Gallinaro
Israel J. Math. 2024
A geometric approach to some systems of exponential equations, Vahagn Aslanyan, Jonathan Kirby and Vincenzo Mantova
IMRN 2022
On systems of equations in abelian varieties, Francesco Gallinaro
IMRN 2023
Solutions of equations involving the modular j-function, Sebastian Eterović and Sebastián Herrero
Trans. Amer. Math. Soc. 2021
Solving systems of equations of raising-to-powers type, Francesco Gallinaro
Israel J. Math. 2024
Differential existential closedness for the j-function, Vahagn Aslanyan, Sebastian Eterović and Jonathan Kirby
Proc. Amer. Math. Soc. 2021
Generic solutions of equations involving the modular j-function, Sebastian Eterović
preprint 2022
Blurrings of the j-function, Vahagn Aslanyan and Jonathan Kirby
The Quarterly Journal of Mathematics, 2022
A closure operator respecting the modular j-function, Vahagn Aslanyan, Sebastian Eterović and Jonathan Kirby
Israel J. Math. 2023
Equations involving the modular j-function and its derivatives, Vahagn Aslanyan, Sebastian Eterović and Vincenzo Mantova
Preprint 2023
Algebraic varieties and automorphic functions, Sebastian Eterović and Roy Zhao
preprint 2021
Some equations involving the Gamma function, Sebastian Eterović and Adele Padgett
To appear in Trans. Amer. Math. Soc. 2024
The theory of exponential equations of semi-abelian varieties, Jonathan Kirby
Selecta Math. (N.S.) 2009
Exponentially closed fields and the conjecture on intersections with tori, Jonathan Kirby and Boris Zilber
Ann. Pure Appl. Logic 2014
Some remarks on atypical intersections, Vahagn Aslanyan
Proc. Amer. Math. Soc. 2021
O-minimality and the André—Oort conjecture for C^n, Jonathan Pila
Ann. of Math. 2011
Some unlikely intersections beyond André—Oort, Philipp Habegger and Jonathan Pila
Compos. Math. 2012
O-minimality and certain atypical intersections, Philipp Habegger and Jonathan Pila
Sci. Éc. Norm. Supér. 2016
Some remarks on atypical intersections, Vahagn Aslanyan
Proc. Amer. Math. Soc. 2021
Weak modular Zilber—Pink with derivatives, Vahagn Aslanyan
Math. Ann. 2022
A note on unlikely intersections in Shimura varieties, Vahagn Aslanyan and Christopher Daw
Journal of Number Theory 2024
Multiplicative relations among differences of singular moduli, Vahagn Aslanyan, Sebastian Eterović and Guy Fowler
preprint 2023
Applications of the hyperbolic Ax—Schanuel conjecture, Christopher Daw and Jinbo Ren
Compositio Math. 2018
The André-Oort conjecture for A_g, Jacob Tsimerman
Ann. of Math. 2018
Canonical heights on Shimura varieties and the André—Oort conjecture, Jonathan Pila, Ananth Shankar, Jacob Tsimerman, Hélène Esnault, Michael Groechenig
preprint 2021
Effective transcendental Zilber—Pink for variations of Hodge-structure, Jonathan Pila and Thomas Scanlon
preprint 2021
On the distribution of the Hodge loci, Gregorio Baldi, Bruno Klingler and Emmanuel Ullmo
Invent Math. 2024
Likely intersections, Sebastian Eterović and Thomas Scanlon
preprint 2022
Existence and density of typical Hodge loci, Nazim Khelifa and David Urbanik
preprint 2023
Compact subvarieties of the moduli space of complex abelian varieties, Samuel Grushevsky, Gabriele Mondello, Riccardo Salvati Manni and Jacob Tsimerman
preprint 2024
On Schanuel's conjecture, James Ax
Ann. of Math. 1971
Périodes de 1-motifs et transcendance, Cristiana Bertolin
J. Number Theory 2002
The uniform Schanuel conjecture of the real numbers, Jonathan Kirby and Boris Zilber
Bull. Lond. Math. Soc. 2006
Exponential algebraicity in exponential fields, Jonathan Kirby
Bull. Lond. Math. Soc. 2010
A Schanuel property for exponentially transcendental powers, Martin Bays, Jonathan Kirby and Alex Wilkie
Bull. Lond. Math. Soc. 2010
Ax-Schanuel for the j-function, Jonathan Pila and Jacob Tsimerman
Duke Math. J. 2015
A Schanuel property for j, Sebastian Eterovic
Bull. Lond. Math. Soc. 2018
Schanuel type conjectures and disjointness, Isaac Broudy and Sebastian Eterovic
Ramanujan J. 2023
Some topics in differential algebraic geometry I: analytic subgroups of algebraic groups, James Ax
Am. J. Math. 1972
Ax-Schanuel for Shimura varieties, Ngaiming Mok, Jonathan Pila and Jacob Tsimerman
Ann. of Math. 2019
The Ax-Schanuel conjecture for variations of Hodge structures, Benjamin Bakker and Jacob Tsimerman
Invent. Math. 2019
The Ax-Schanuel conjecture for variations of mixed Hodge structures, Ziyang Gao and Bruno Klingler
Math. Ann. 2023
A differential approach to the Ax—Schanuel I, David Blasquez-Sans, Guy Casale, James Freitag and Ronnie Nagloo
preprint 2021
Functional transcendence of periods and the geometric André—Grothendieck period conjecture, Benjamin Bakker and Jacob Tsimerman
preprint 2022
Ax-Schanuel for variations of mixed Hodge structures, Kenneth Chiu
preprint 2022
Mixed Ax-Schanuel with derivatives for mixed period mappings, Kenneth Chiu
preprint 2021
Categoricity of modular and Shimura curves, Christopher Daw and Adam Harris
J. Inst. Math. Jussieu, 2017
Pseudo-exponential maps, variants and quasiminimality, Martin Bays and Jonathan Kirby
Algebra & Number Theory 2018
Universal covers of commutative finite Morley rank groups, Martin Bays, Bradd Hart and Anand Pillay
J. Inst. Math. Jussieu 2020
Categoricity of Shimura varieties, Sebastian Eterovic
preprint 2018
Zilber's notion of logically perfect structures, John T. Baldwin and Andrés Villaveces
Model Theory 2024