Geodesic
Kronecker's limit formula in a~real quadratic field
Izvestiya. Mathematics , Tome 17 (1981) no. 1, pp. 147-176.

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In this paper the author obtains a formula representing the free term of the Laurent expansion of the zeta functions of absolute and ray classes of a real quadratic field at the point 1, as well as the value of Hecke's $L$-function corresponding to the signature character. The formula contains Dedekind sums and sums analogous to them in which functions depending on the same arguments as in ordinary Dedekind sums appear. Bibliography: 4 titles. 
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A. P. Novikov. Kronecker's limit formula in a~real quadratic field. Izvestiya. Mathematics , Tome 17 (1981) no. 1, pp. 147-176. http://geodesic.mathdoc.fr/item/IM2_1981_17_1_a6/

[1] Beitmen G., Erdein A., Vysshie transtsendentnye funktsii, Nauka, M., 1973

[2] Meyer C., Die Berechnung der Klassenzahl abelscher Körper über quadratischen Zahlkörpern, Akademie-Verlag, Berlin, 1957 | MR | Zbl

[3] Zagier D., “A Kronecker limit formula for real quadratic fields”, Math. Ann., 213:2 (1975), 153–184 | DOI | MR | Zbl

[4] Shintani T., “On a Kronecker limit formula for real quadratic fields”, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 24:1 (1977), 167–199 | MR | Zbl