Class Numbers and Iwasawa Invariants of Certain Totally Real Number Fields Original Research Article

Let p be an odd regular prime number. We prove that there exist infinitely many totally real number fields k of degree p−1 whose class numbers are not divisible by p. Moreover, for certain regular prime number p, we prove that there exist infinitely many totally real number fields k of degree p−1 whose Iwasawa λp-, μp-invariants vanish.