Units in arithmetic progression in an algebraic number field

Newman, Morris

doi:10.1090/S0002-9939-1974-0330101-2

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Units in arithmetic progression in an algebraic number field
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Proc. Amer. Math. Soc. 43 (1974), 266-268 Request permission

Abstract:

It is shown that a given algebraic number field of degree $n \geqq 4$ over the rationals can contain at most $n$ units in arithmetic progression, and that this bound is sharp.

References

Morris Newman, Units in cyclotomic number fields, J. Reine Angew. Math. 250 (1971), 3–11. MR 288098, DOI 10.1515/crll.1971.250.3
Morris Newman, Diophantine equations in cyclotomic fields, J. Reine Angew. Math. 265 (1974), 84–89. MR 337889, DOI 10.1515/crll.1974.265.84
G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis, Dover Publications, New York, N.Y., 1945 (German). MR 0015435