Riemann-Hurwitz formula in basic $ℤ_S$-extensions

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Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China

N. Childress, λ-invariants and Γ-transforms, Manuscripta Math. 64 (1989), 359-375.
E. Friedman, Ideal class groups in basic $ℤ_{p}_1 \times ... \times ℤ_{p}_s$ extensions of abelian number fields, Invent. Math. 65 (1982), 425-440.
K. Iwasawa, On Γ-extensions of algebraic number fields, Bull. Amer. Math. Soc. 65 (1959), 183-226.
K. Iwasawa, Riemann-Hurwitz formula and p-adic Galois representations for number fields, Tohôku Math. J. (2) 33 (1981), 263-288.
Y. Kida, l-extensions of CM-fields and cyclotomic invariants, J. Number Theory 2 (1980), 519-528.
J. Satoh, The Iwasawa $λ_{p}$ -invariants of Γ-transforms of the generating functions of the Bernoulli numbers, Japan. J. Math. 17 (1991), 165-174 .
W. Sinnott, On the μ-invariant of the Γ-transform of a rational function, Invent. Math. 75 (1984), 273-282.
W. Sinnott, On the p-adic L-functions and the Riemann-Hurwitz genus formula, Compositio Math. 53 (1984), 3-17.
W. Sinnott, Γ-transforms of rational function measures on $ℤ_{S}$ , Invent. Math. 89 (1987), 139-157.
L. C. Washington, Introduction to Cyclotomic Fields, Grad. Texts in Math. 83, Springer, 1982.