Date:
Tue, 18/11/202514:00-15:00
Location:
Ross 70
Title: Real numbers and Laurent series are sums with diverging partial quotients
Abstract: Define the set
G := {α ∈ R \ Q : an(α) →∞} ∪ Q ,
where an(α) is the n-th partial quotient in the continued fraction expansion of α. In a joint paper with Erez Nesharim, we showed that G + G = R.
Recently, we also proved an analogous statement for the Laurent series over an arbitrary eld. Our proof is based on an algorithm that was recently developed by Nikita Shulga.
Abstract: Define the set
G := {α ∈ R \ Q : an(α) →∞} ∪ Q ,
where an(α) is the n-th partial quotient in the continued fraction expansion of α. In a joint paper with Erez Nesharim, we showed that G + G = R.
Recently, we also proved an analogous statement for the Laurent series over an arbitrary eld. Our proof is based on an algorithm that was recently developed by Nikita Shulga.