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SUMMARY:Values of the Ramanujan tau-function - Vandita Patel (Manchester U
 niversity)
DTSTART:20230516T133000Z
DTEND:20230516T143000Z
UID:TALK200365@talks.cam.ac.uk
CONTACT:Rong Zhou
DESCRIPTION:The infamous Ramanujan tau-function is the starting point for 
 many mysterious conjectures and difficult open problems within the realm o
 f modular forms. In this talk\, I will discuss some of our recent results 
 pertaining to odd values of the Ramanujan tau-function. We use a combinati
 on of tools which include the Primitive Divisor Theorem of Bilu\, Hanrot a
 nd Voutier\, bounds for solutions to Thue–Mahler equations due to Bugeau
 d and Gyory\, and the modular approach via Galois representations of Frey-
 Hellegouarch elliptic curves. This is joint work with Mike Bennett (UBC)\,
  Adela Gherga (Warwick) and Samir Siksek (Warwick).
LOCATION:MR15
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