Arithmetic progressions in binary quadratic forms and norm forms

Christian Elsholtz; Christopher Frei

doi:10.1112/blms.12256

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.

Original language	English
Journal	Bulletin of the London Mathematical Society
Early online date	6 May 2019
DOIs	https://doi.org/10.1112/blms.12256
Publication status	Published - 2019

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title = "Arithmetic progressions in binary quadratic forms and norm forms",

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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SN - 0024-6093

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

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Arithmetic progressions in binary quadratic forms and norm forms

Abstract

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