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DTSTART:20070311T020000
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DTSTAMP:20260527T111038
DTSTART;TZID=America/Detroit:20260609T110000
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SUMMARY:Presentation:Modular degree of elliptic curves over function fields in relation to Jacquet-Langlands
DESCRIPTION:Abstract:\n\nIn this thesis\, we study the geometry of automorphic forms in the function field setting. The primary goal of this thesis prove a formula relating degrees of modular parametrization of an elliptic curve by different Drinfeld modular curves. This is analogous to the similar result of Ribet-\nTakahashi [RT97] in the number field setting\, which relates degrees of modular parameterizations of an elliptic curve over Q by varying Shimura curves. To prove this result\, I prove a result analogous to Ribet’s short exact sequence [Rib90a] which relates the special fibers of Shimura varieties at different primes. Using this technical result I deduce (in the function field case) level-lowering results akin to those of Ribet [Rib90a] and relations between Petersson inner products of modular forms that are related by the Jacquet-Langlands correspondence similar to the work of K. Prasanna [Pra03].
UID:148433-21904254@events.umich.edu
URL:https://events.umich.edu/event/148433
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Dissertation,Graduate,Graduate Students,Mathematics
LOCATION:Off Campus Location
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