Date: Monday, June 06, 2022
Location: Hybrid East Hall (2:00 PM to 4:00 PM)
Title: Hilbert's Inequality, Generalized Factorials, and Partial Factorizations of Generalized Binomial Products
Abstract:
In Person: 3096 East Hall
Zoom Link: https://umich.zoom.us/j/95283305303?pwd=Nmc2V1hiZmZidHVxdGpBTGdjaUtadz09
Meeting ID: 952 8330 5303
Passcode: 120960
This dissertation treats three topics in number theory. The first topic concerns the problem of determining the optimal constant in the Montgomeryâ€“Vaughan weighted generalization of Hilbert's inequality. The second topic presents a further generalization of Bhargava's generalized factorials in the ring Z. We define invariants associated to all pairs (S, b) of a nonempty subset S of Z and a nontrivial proper ideal b in Z and use them to construct generalized factorials. The third topic is asymptotics of partial factorizations of products of generalized binomial coefficients constructed using generalized factorials from the second topic.
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Speaker: Wijit Yangjit
Institution: UM
Event Organizer:
