Norm Form Equations and Linear Divisibility Sequences

Abstract: Finding integer solutions to norm form equations is a classic Diophantine problem. Using the units of the associated coefficient ring, we can produce sequences of solutions to these equations. It turns out that these solutions can be written as tuples of linear homogeneous recurrence sequences, each with characteristic polynomial equal to the minimal polynomial of our unit. We show that for certain families of norm forms, these sequences are linear divisibility sequences.

number theory

Audience: researchers in the discipline

POINT: New Developments in Number Theory

Series comments: There will be two 20-minute contributed talks during each meeting aimed at a general number theory audience, including graduate students.

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