Mathematical Work
Lang studied under Emil Artin at Princeton University, writing his thesis on quasi-algebraic closure. Lang then worked on the geometric analogues of class field theory and diophantine geometry. Later he moved into diophantine approximation and transcendence theory, proving the Schneider–Lang theorem.
A break in research while he was involved in trying to meet 1960s student activism halfway caused him (by his own description) difficulties in picking up the threads afterwards. He wrote on modular forms and modular units, the idea of a 'distribution' on a profinite group, and value distribution theory.
He made a number of conjectures in diophantine geometry: Mordell–Lang conjecture, Bombieri–Lang conjecture, Lang's integral point conjecture, Lang–Trotter conjecture, Lang conjecture on Gamma values, Lang conjecture on analytically hyperbolic varieties.
He introduced the Lang map and the Lang–Steinberg theorem in algebraic groups.
He introduced the Katz–Lang finiteness theorem.
Read more about this topic: Serge Lang
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