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NCTS Number Theory Seminar
 
12:00 - 13:00, December 3, 2021 (Friday)
Cisco Webex, Online seminar
(線上演講 Cisco Webex)
Modular Knots, Automorphic Forms, and the Rademacher Symbols for Triangle Groups
Toshiki Matsusaka (Nagoya University)

Abstract:

In a celebrated paper “Knots and dynamics”, Étienne Ghys proved that the linking numbers of modular knots and the missing trefoil in coincide with the values of a highly ubiquitous function called the Rademacher symbol for . In this talk, we replace by the triangle group for any coprime pair $(p,q)$ of integers with . We invoke the theory of harmonic Maass forms for to introduce the notion of the Rademacher symbol and provide several characterizations. Among other things, we generalize Ghys’s theorem for modular knots around any missing torus knot in and in a lens space. This is joint work with Jun Ueki (Tokyo Denki University).
 
 
JOIN WEBEX MEETING
Meeting number (access code): 2511 219 9519
Meeting password: fYXUxBfi447 (39989234 from phones and video systems)


 

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