2010
DOI: 10.1142/s1793042110002818
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Arithmetic Traces of Non-Holomorphic Modular Invariants

Abstract: We extend results of Bringmann and Ono that relate certain generalized traces of Maass–Poincaré series to Fourier coefficients of modular forms of half-integral weight. By specializing to cases in which these traces are usual traces of algebraic numbers, we generalize results of Zagier describing arithmetic traces associated to modular forms. We define correspondences [Formula: see text] and [Formula: see text]. We show that if f is a modular form of non-positive weight 2 - 2 λ and odd level N, holomorphic awa… Show more

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Cited by 31 publications
(42 citation statements)
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“…After this paper was written, we learned that results similar to some of those presented here were obtained independently in [Miller and Pixton 2007]. We thank the referee for some helpful comments.…”
Section: Acknowledgmentssupporting
confidence: 66%
“…After this paper was written, we learned that results similar to some of those presented here were obtained independently in [Miller and Pixton 2007]. We thank the referee for some helpful comments.…”
Section: Acknowledgmentssupporting
confidence: 66%
“…Remark. Note that these results generalize works of Duke and Jenkins [DJ08] and Miller and Pixton [MP10]. We also obtain the results in Section 9 of [Zag02] as a special case.…”
Section: Introduction and Statement Of Resultssupporting
confidence: 83%
“…We apply this to F (z) which is a weight −2 weakly holomorphic modular form, a meromorphic modular form whose poles are supported at cusps. Theorem 3.6 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.…”
mentioning
confidence: 99%