References
Apostol, T.: Generalized Dedekind sums and transformation formulae of certain Lambert series. Duke Math. J.17, no. 2, 147–157 (1950)
Coates, J.:p-adicL-functions and Iwasawa’s theory. Pp. 269–353 in Algebraic number fields (ed. by A. Fröhlich), London: Academic Press 1977
Frobenius, G.: Über die Bernoullischen Zahlen und die Eulerschen Polynome. Sitzungsber. Königl. Preuss. Akad. Wiss. Berlin, 809–847 (1910); pp. 440–478 in Gesammelte Abhandlungen III, Berlin-Heidelberg-New York: Springer 1968.
Jakubec, S.: On divisibility of class number of real abelian fields of prime conductor. Abh. Math. Sem. Univ. Hamburg63, 67–86 (1993)
Jakubec, S.: On the divisibility ofh + by the prime 3. Rocky Mountain J. Math.24, no. 4, 1467–1473 (1994)
Jakubec, S.: On divisibility ofh + by the prime 5. Math. Slovaca44, no. 5, 651–661 (1994)
Jakubec, S.: Connection between the Wieferich congruence and divisibility ofh +. Acta Arith.71, no. 1, 55–64 (1995)
Jakubec, S.: Connection between congruencesn q−1 ≡ 1 (modq 2) and divisibility ofh +. Abh. Math. Sem. Univ. Hamburg66, 151–158 (1996)
Jakubec, S.: On divisibility of the class numberh + of the real cyclotomic fields of prime degreel. Math. Comp. (to appear)
Jakubec, S. and Louboutin, S., personal communication
Jakubec, S. and Trojovský, P.: On divisibility of the class numberh + of the real cyclotomic fields\(\mathbb{Q}(\zeta _p + \zeta _p ^{ - 1} )\) by primesq<5000. (Manuscript)
Leopoldt, H.-W.: Über Klassenzahlprimteiler reeller abelscher Zahlkörper als Primteiler verallgemeinerter Bernoullischer Zahlen. Abh. Math. Sem. Univ. Hamburg23, 36–47 (1959)
Leopoldt, H.-W.: Über Fermatquotienten von Kreiseinheiten und Klassenzahlformeln modulop. Rend. Circ. Mat. Palermo (2)9, 39–50 (1960)
Leopoldt, H.-W.: Zur Arithmetik in abelschen Zahlkörpern. J. Reine Angew. Math.209, 54–71 (1962)
Leopoldt, H.-W.: Einep-adische Theorie der Zetawerte, II. Diep-adischeΓ-Transformation. J. Reine Angew. Math.274/275, 224–239 (1975)
Slavutski, I. Sh.:L-functions and the class number of cyclotomic fields (Russian). Uspekhi Mat. Nauk43, no. 5 (263), 215–216 (1988)
Washington, L. C.: Introduction to cyclotomic fields, 2nd ed. (Graduate texts in mathematics, 83) New York-Berlin-Heidelberg: Springer 1996
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Metsänkylä, T. An application of thep-adic class number formula. Manuscripta Math 93, 481–498 (1997). https://doi.org/10.1007/BF02677487
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DOI: https://doi.org/10.1007/BF02677487