Open Diophantine problems
By Michel Waldschmidt. 2003
75 citations recorded by the source corpus.
Diophantine Analysis is a very active domain of mathemat- ical research where one finds more conjectures than results. We collect here a number of open questions concerning Diophantine equations (including Pillai's Conjectures), Diophantine approximation (featuring the abc Conjecture) and transcendental number theory (with, for instance, Schanuel's Conjecture). Some questions related to Mahler's measure and Weil absolute logarithmic height are then considered (e.g., Lehmer's Problem). We also discuss Mazur's question regarding the density of rational points on a variety, especially in the particular case of algebraic groups, in connexion with transcendence problems in several variables. We say only a few words on metric problems, equidistribution questions, Diophantine approximation on manifolds and Diophantine analysis on function fields. 2000 Math. Subj. Class. Primary 11Jxx; Secondary 11Dxx, 11Gxx, 14Gxx.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3d59f5251d4c7419375811afecb5f4ab62bda84d
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Transcendence of Periods: The State of the Art (2006, background): “…of elliptic curves, C. Bertolin [9] rephrased Andr´e’s conjecture more explicitly by stating her elliptico-toric conjecture, which contains the expected transcendence and algebraic independence results concerning the values of the exponential function, of the Weierstrass ℘ and ζ functions,…”