Cyclotomic invariants and 𝐸-irregular primes

Abstract

We prove some general results about the Iwasawa invariants λ − {\lambda ^ - } and μ − {\mu ^ - } of the 4pth cyclotomic field (p an odd prime), and determine the values of these invariants for p > 10 4 p > {10^4} . The properties of λ − {\lambda ^ - } and μ − {\mu ^ - } are closely connected with the E-irregularity (i.e. the irregularity with respect to the Euler numbers) of p. A list of all E-irregular primes less than 10 4 {10^4} , computed by the first author, is included and analyzed.