Finiteness theorems with almost prime inputs

Abstract: The Conway–Schneeberger Fifteen theorem states that a given positive definite integral quadratic form is universal (i.e., represents every positive integer with integer inputs) if and only if it represents the integers up to 15. This theorem is sometimes known as “Finiteness theorem" as it reduces an infinite check to a finite one. In this talk, I would like to present my recent work along with Ben Kane where I have investigated quadratic forms which are universal when restricted to almost prime inputs and have established finiteness theorems akin to the Conway–Schneeberger Fifteen theorem.

classical analysis and ODEscombinatoricsnumber theory

Audience: researchers in the topic

Special Functions and Number Theory seminar

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