A sufficient condition for Leopoldt's conjecture

✍ Scribed by Norikazu Kubotera

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 168 KB
• Volume: 111
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2004.07.019

✦ Synopsis

In this paper, by using an analogue of theorems of Iwasawa (Kenkichi Iwasawa Collected Papers, vol. 2, Springer, Berlin, 2001, pp. 862-870) we give a sufficient condition for Leopoldt's conjecture (J. Reine Angew. Math. 209 (1962) 54) on the non-vanishing of the p-adic regulator of an algebraic number field. Using this sufficient condition we are able to prove Leopoldt's conjecture for several non-Galois extensions over the rational number field Q.