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NT&AG: Hillel Firstenberg (HUJI), "Hyper-modular functions, irrationality of \zeta(3), and algebraic functions over finite fields" | Einstein Institute of Mathematics

NT&AG: Hillel Firstenberg (HUJI), "Hyper-modular functions, irrationality of \zeta(3), and algebraic functions over finite fields"

Date: 
Mon, 04/06/201814:00-15:00
Location: 
Room 70A, Ross Building, Jerusalem, Israel
Using formal power series one can define, over any field, a class of functions including algebraic and classical modular functions over C. Under simple conditions the power series will have coefficients in a subring of the field - say Z - and this plays a role in Apery's proof of the irrationality of \zeta(3). Remarkably over a finite field all such functions/power series are algebraic.
I will call attention to a natural - but open - problem in this area.