On the Class-number of the Maximal Real Subfield of a Cyclotomic Field. Issue 7 (4th November 2016)

• Record Type: Journal Article
• Authors: Hoque, Azizul; Saikia, Helen K.
• Is Part Of: Quaestiones mathematicae. Volume 39:Issue 7(2016)
• Page Start: 889
• Page End: 894
• Publication Date: 2016-11-04
• Subjects: 11R29 -- 11R18 -- 11R11; Maximal real subfield of cyclotomic field -- real quadratic field -- class number; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2016.1188864
• Languages: English
• ISSNs: 1607-3606

Abstract

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 .