Abstract
Consideration of the analytic continuation of the Eisenstein series of weight 3/2 for the group Γ0(4) leads to a new proof of Mordell's formula connecting the values X(ω)=∑ ∞m=1 F(m)eπimω, Imω > 0, and χ(−1/ω). The behavior of the function χ(ω) for Γ0(4) is examined by the same method.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 64, pp. 69–79, 1976.
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Golubeva, E.P., Fomenko, O.M. Series ∑F(m)qm, where F(m) is the number of odd classes of binary quadratic forms of determinant −m. J Math Sci 17, 1759–1766 (1981). https://doi.org/10.1007/BF01091762
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DOI: https://doi.org/10.1007/BF01091762