Eichler–Shimura theory for mock modular forms

Bringmann, Kathrin; Guerzhoy, Pavel; Kent, Zachary A.; Ono, Ken

doi:10.1007/s00208-012-0816-y

Cited by 45 publications

(67 citation statements)

References 25 publications

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“…The surjectivity of the restricted map r : S ! k → W k was established in [1]. This together with the observation in [7] that r(G k ; z) ∈ W k \W k gives us exactness of the sequence at…”

Section: Even and Odd Functions This Splitting Induces Further Splitmentioning

confidence: 65%

“…In this case, the integrals in (1) and (2) may be divergent. In [1], Bringmann, Guerzhoy, Ono, and the author found a way to avoid this obstruction by considering the formal Eichler integral of f given by…”

mentioning

confidence: 99%

“…It was noticed, in [1], that by restricting to forms in S ! k , the period functions in (4) are actually polynomials.…”

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confidence: 99%

“…With respect to previous work relating periods to L-values [1,5,6,7], we would like to interpret the "extra periods" in (4) in terms of the L-series for G k . We do this by following Zagier in [7].…”

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confidence: 99%

“…It is natural to consider an Eichler-Shimura isomorphism in this context extending the work of [1,5,7]. In this direction, let V k be the space of polynomials in z of degree at most k − 2, and define the larger space …”

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confidence: 99%

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Periods of Eisenstein series and some applications

Kent

2011

Proc. Amer. Math. Soc.

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Abstract. Bringmann, Guerzhoy, Ono, and the author developed an EichlerShimura theory for weakly holomorphic modular forms by studying associated period polynomials. Here we include the Eisenstein series in this theory.Classically, the periods of a weight k (k ≥ 4 will always denote an even integer) cusp form f = l≥1 a f (l)q l (q := e 2πiτ with τ = x + iy ∈ C with y > 0) on Γ := SL 2 (Z) are given byThese periods appear in the coefficients of the period polynomial of f defined by

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Section: Even and Odd Functions This Splitting Induces Further Splitmentioning

confidence: 65%

mentioning

confidence: 99%

“…It was noticed, in [1], that by restricting to forms in S ! k , the period functions in (4) are actually polynomials.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%