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Units in arithmetic progression in an algebraic number field


Author: Morris Newman
Journal: Proc. Amer. Math. Soc. 43 (1974), 266-268
MSC: Primary 12A45
DOI: https://doi.org/10.1090/S0002-9939-1974-0330101-2
MathSciNet review: 0330101
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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 [Enhancements On Off] (What's this?)

  • [1] M. Newman, Units in cyclotomic number fields, J. Reine Angew. Math. 250 (1971), 3-11. MR 44 #5296. MR 0288098 (44:5296)
  • [2] -, Diophantine equations in cyclotomic fields, J. Reine Angew. Math. (to appear). MR 0337889 (49:2658)
  • [3] G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis, Springer, Berlin, 1925; photographic reproduction, Vols. I, II, Dover, New York, 1945. MR 7, 418. MR 0015435 (7:418e)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0330101-2
Keywords: Algebraic number fields, units
Article copyright: © Copyright 1974 American Mathematical Society

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