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arXiv · 1810.11251

Arithmetic progressions in binary quadratic forms and norm forms

Christian Elsholtz·Christopher Frei
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Abstract

We prove an upper bound for the length of an arithmetic progression represented by an irreducible integral binary quadratic form or a norm form, which depends only on the form and the progression's common difference. For quadratic forms, this improves significantly upon an earlier result of Dey and Thangadurai.

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Christian Elsholtz, Christopher Frei. 2018-10-26. Arithmetic progressions in binary quadratic forms and norm forms. https://doi.org/10.1112/blms.12256

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