On the Class-number of the Maximal Real Subfield of a Cyclotomic Field. Issue 7 (4th November 2016) - Hoque, Azizul; Saikia, Helen K.
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 .