Hankel determinants and continued fractions for hyperelliptic functions

Speaker: 

Andrew Hone

Affiliation: 

University of Kent

Date: 

Wed, 19/06/2019 - 2:00pm

Venue: 

RC-4082, The Red Centre, UNSW

Abstract: 

Three-term linear recurrences are a central part of the theory of continued fractions, in the description of convergents, as well as being a feature of orthogonal polynomials. In this talk we consider some examples of discrete dynamical systems associated with continued fraction expansions in hyperelliptic function fields. The case of ellliptic curves corresponds to a well known example of the QRT map associated withthe Somos-4 recurrence, and connects Hankel determinant formulae found by Chang, Hu & Xin with earlier work of van der Poorten. For the case of genus two and higher, new discrete integrable systems will be presented, with associated Hankel determinant formulae, and the connection with three-term linear relations and orthogonal polynomials will briefly be mentioned.

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