References
M. Deuring: Automorphismen und Divisorenklassen der Ordnung L in algebraischen Funktionenkörpern, Math. Ann. 113, 208–215 (1936)
H. Hasse: Vorlesungen über Klassenkörpertheorie, Physica-Verlag. Wurzburg, 1967
K. Iwasawa; Riemann-Hurwitz formula and p-adic Galois representations for number fields, Tôhoku Mathematical Journal, vol. 33; no. 2, June 1981, 263–288
Y. Kida: L-extensions of CM-fields and cyclotomic invariants, Journal of Number Theory 12 (1980), 519–528
Y. Kida: Cyclotomic ℤp -extensions of J-fields, Journal of Number Theory 14, 340–352 (1982)
M. L. Madan: On a theorem of M. Deuring and I. R. Safarevic, Manuscripta Math. 23, 91–102 (1977)
M. L. Madan and Sat Pal: Galois cohomology and a theorem of E. Artin, Number Theory and Algebra, © 1977 Academic Press, Inc.
M. Moriya; Über die Struktur der Divisorenklassen einer zyklischen Erweiterung von Primzahlgrad über einem algebraischen Funktionenkörper, Tôhoku Math. J. 48 (1941), 43–54
I. R- Šafarevič: On p-extensions, Amer. Math. Soc. Trans. Series II, vol. 4, 59–71 (1954)
W. Sinnott: On p-adic L-functions and the Riemann-Hurwitz genus formula (preprint)
E. Weiss: Cohomology of Groups, Academic Press (1969)
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D'Mello, J.G., Madan, M.L. Class group rank relations in\(\mathop {ZZ}\limits_\ell \)-extensions. Manuscripta Math 41, 75–107 (1983). https://doi.org/10.1007/BF01165930
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DOI: https://doi.org/10.1007/BF01165930