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Michael Mertens (2014)
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Michael Mertens (2013)
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Brandon Williams (2017)
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For any number $$m \equiv 0,1 \, (4)$$ m ≡ 0 , 1 ( 4 ) , we correct the generating function of Hurwitz class number sums $$\sum _r H(4n - mr^2)$$ ∑ r H ( 4 n - m r 2 ) to a modular form (or quasimodular form if m is a square) of weight two for the Weil representation attached to a binary quadratic form of discriminant m and determine its behavior in the Petersson scalar product. This modular form arises through holomorphic projection of the zero-value of a nonholomorphic Jacobi Eisenstein series of index 1 / m. When m is prime, we recover the classical Hirzebruch–Zagier series whose coefficients are intersection numbers of curves on a Hilbert modular surface. Finally, we calculate certain sums over class numbers by comparing coefficients with an Eisenstein series.
Research in the Mathematical Sciences – Springer Journals
Published: May 7, 2018
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