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In a little-known paper Hurwitz gave an infinite series representation of the class number for positive definite binary quadratic forms. In this paper we give a similar formula in the indefinite case. We also give a simple proof of Hurwitz’s formula and indicate some extensions.
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William Duke, Özlem Imamoglu, Árpad Tóth, On a class number formula of Hurwitz. J. Eur. Math. Soc. 23 (2021), no. 12, pp. 3995–4008DOI 10.4171/JEMS/1097