Traces of singular moduli

By Don Zagier. 2002

259 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/12848f0754d20e2c09c30277eda3150619705bc7

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Citations in the corpus

Unearthing the visions of a master: harmonic Maass forms and number theory (2008, background): “Zagier’s work has inspired an enormous number of works [54, 58, 64, 65, 77, 78, 87, 88, 89, 95, 127, 128, 154] by the author, Bringmann, Bruinier, D.”
Hilbert class polynomials and traces of singular moduli (2006, methodology): “(Existence and uniqueness follow from Lemma 14.2 of [B1]; see also Section 4 of [ Z1 ]).”
Cycle integrals of the j-function and mock modular forms (2011, background): “Theorem 2 generalizes to the case dD > 0 known results of Borcherds [2] and Zagier [ 49 ].”
Fourier interpolation on the real line (2017, unknown): “Note that generating functions very similar to (19) have also been used in [20] in the computation of traces of singular moduli.”
Zagier-type dualities and lifting maps for harmonic Maass–Jacobi forms (2010, background): “Zagier [24] established a striking duality for Fourier coefficients of weakly holomorphic modular forms.”
Integral traces of singular values of weak Maass forms (2008, methodology): “Furthermore, when s = 2, 3, 4, 5, 7, Theorem 1 can also be deduced from results of [Zagier 2002].”
Traces of CM values of modular functions (2004, background): “Introduction In [25], Zagier considers the normalized Hauptmodul J(z) = j(z) − 744 for the group Γ(1) = PSL2(Z), where j(z) = e −2πiz + 744 + 196884e + .”
Modular functions and the uniform distribution of CM points (2006, methodology): “It is clear from (8) that the Fourier coefficient B(d) is zero unless d · 0;3 (mod4): Zagier [ 22 ] proved the following striking connection between the traces of singular moduli and the coefficients B(d):”
Heegner divisors, $L$-functions and harmonic weak Maass forms (2007, methodology): “The expansions of the first few fd are given in [ Za2 ], and one sees that the coefficients are rational.”
Regularized theta liftings and periods of modular functions (2011, background): “For any function f on M , we then define the trace following [29] and [5] by (3.”
Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms (2011, background): “6 is a new result which adds to the extensive literature (for example, see [5, 9, 10, 13, 14, 15, 22, 29, 30]) inspired by Zagier’s seminal paper [34] on “traces” of singular moduli.”