Conference Prix CRM-FIELDS-PIMS 2017
Professor Henri Darmon will be giving a presentation titled: ""p-adic Analysis and Hilbert's Twelfth Problem" at the at UdeM听on October 6th, 2017.听
Abstract:听Modular functions play an important role in many aspects of number theory. The theory of complex multiplication, one of the grand achievements of the subject in the 19th century, asserts that the values of modular functions at quadratic imaginary arguments generate (essentially all) abelian extensions of imaginary quadratic fields. Hilbert's twelfth problem concerns the generalisation of this theory to other base fields. I will describe an ongoing work in collaboration with Jan Vonk which identifies a class of functions that seem to play the role of modular functions for real quadratic fields. A key difference with the classical setting is that they are meromorphic functions of a p-adic variable (defined in the framework of "rigid analysis" introduced by Tate) rather than of a complex variable.
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Le caf茅 sera servi 脿 15h30 et une r茅ception suivra la conf茅rence au Salon Maurice-L鈥橝bb茅 (salle 6245).
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Coffee will be served before the conference and a reception will follow at Salon Maurice-L鈥橝bb茅 (Room 6245).