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The Class Number Formula of a Real Quadratic Field and an Estimate of the Value of a Unit

  • T. Mitsuhiro (a1), T. Nakahara (a2) and T. Uehara

Abstract

Our aim is to give an arithmetical expression of the class number formula of real quadratic fields. Starting from the classical Dirichlet class number formula, our proof goes along arithmetical lines not depending on any analytical method such as an estimate for

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References

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1. Bergstrom, H., Die Klassenzahlformel für réelle quadratische Zahlkörper mit zusammengesetzer Diskriminante als Produkt verallgemeinerter Gaufischer Summen, J. Reine Angew. Math. 186(1945), 91115.
2. Chowla, P., On the class-number of real quadratic fields, J. Reine Angew. Math. 230(1968), 5160.
3. Chowla, P. and Chowla, S., Formulae for the units and class-numbers of real quadratic fields, J. Reine Angew. Math. 230(1968), 6165.
4. Hasse, H., Vorlesungen Über Zahlentheorie, Springer Verlag, Berlin, Gôttingen, Heidelberg, New York, 1964.
5. Mitsuhiro, T., A combinatorial proof of an arithmetical expression of Dirichlet's class number formula, Rep. Fac. Sci. Engrg. Saga Univ. Math. 22(1993), 118.
6. Mitsuhiro, T. and Nakahara, T., An arithmetical expression of Dirichlet's class number formula, In: The Proceedings of Analytic Number Theory and Related Topics, World Scientific, Singapore, 1993, 97107, Insertion of Tables, i-iv.
7. Ono, T., A deformation of Dirichlet's class number formula, In: Algebraic Analysis, Vol. II, (eds. Kashiwara, M. and Kawai, T.), Academic Press, Boston, 1988, 659666.
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The Class Number Formula of a Real Quadratic Field and an Estimate of the Value of a Unit

  • T. Mitsuhiro (a1), T. Nakahara (a2) and T. Uehara

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