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SUMMARY:Frank Garvan (University of Florida)
DTSTART:20201001T150000Z
DTEND:20201001T170000Z
DTSTAMP:20260423T035735Z
UID:EIMINT/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EIMINT/4/">A
  new approach to Dyson's rank conjectures</a>\nby Frank Garvan (University
  of Florida) as part of EIMI Number Theory Seminar\n\n\nAbstract\nIn 1944 
 Dyson defined the rank of a partition as the largest part minus the number
  of parts\, and conjectured that the residue of the rank mod 5 divides the
  partitions of 5n+4 into five equal classes. This gave a combinatorial exp
 lanation of Ramanujan's famous partition\ncongruence mod 5. He made an ana
 logous conjecture for the rank mod 7 and the partitions of 7n+5. In 1954 A
 tkin and Swinnerton-Dyer proved Dyson's rank conjectures by constructing s
 everal Lambert-series identities basically using the theory of elliptic fu
 nctions. In 2016 the author gave another proof using the theory of weak ha
 rmonic Maass forms. In this talk we\ndescribe a new and more elementary ap
 proach using Hecke-Rogers series.\n
LOCATION:https://researchseminars.org/talk/EIMINT/4/
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