Article

On the Class-number of the Maximal Real Subfield of a Cyclotomic Field

Published in: Quaestiones Mathematicae
Volume 39 , issue 7 , 2016 , pages: 889–894

DOI: 10.2989/16073606.2016.1188864

Author(s): Azizul Hoque Department of Mathematics, India , Helen K. Saikia Department of Mathematics, India

Keywords: 11R29 , 11R18 , 11R11 , 11R29 , 11R18 , 11R11

Abstract

For any square-free positive integer m, let H(m) be the class-number of the field , where ζ_m is a primitive m-th root of unity. We show that if m = {3(8 g + 5)}² − 2 is a square-free integer, where g is a positive integer, then H(4 m) > 1. Similar result holds for a square-free integer m = {3(8 g +7)}² −2, where g is a positive integer. We also show that n|H(4 m) for certain positive integers m and n.

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