The Theory of Jacobi Forms

By M. Eichler, Don Zagier. 2013

982 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/583886a250f4552c47e089057ce2dcf02db3cb36

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Citations in the corpus

Automorphic Integral Transforms for Classical Groups I: Endoscopy Correspondences (2012, methodology): “o construct such automorphic descents may go back to the classical examples in earlier work ofH. Maass ([Ms79]), ofA. Andrianov ([An79]), of I. Piatetski-Shapiro ([PS83]), of M. Eichler and D. Zagier [EZ85]), and of N. Skoruppa and D. Zagier ([SZ88]), all of which are related to the understanding of”
KUDLA’S MODULARITY CONJECTURE AND FORMAL FOURIER–JACOBI SERIES (2014, neutral): “If g = 1, one can prove this using weak Jacobi forms as in [EZ85].”
The N=1 effective action of F-theory compactifications (2010, neutral): “ction in zK. The key point to note is that Θ(f,N) transforms under (4.4) and the integral shifts of (aκ,˜b κ) such that it cancels the shifts of T0. This allows to identify Θ(f,N) to be a Jacobi form [68]. It is an interesting task to determine explicitly the form of Θ(f,N) for a given Calabi-Yau fo”
Packet structure and paramodular forms (2017, background): “Then they come from elliptic modular forms f1, f2 ∈ S2k−2(SL(2,Z)); see Corollary 1 on page 80 of [6].”
Quantum Black Holes, Wall Crossing, and Mock Modular Forms (2012, background): “(More information about the additive lift can be found in [28].”
A stringy test of the Scalar Weak Gravity Conjecture (2018, background): “According to a classic result [84] the ring of weak Jacobi forms of modular weight w and fugacity index m is freely-generated by two particular weak Jacobi forms,11 φ0,1(τ, z) and φ−2,1(τ, z), over the ring of modular forms C[E4(τ ), E6(τ )].”
Taylor coefficients of mock-Jacobi forms and moments of partition statistics (2014, background): “Such functions were introduced and studied by Eichler and Zagier; see [19] for further background and applications.”
Transfer of Siegel Cusp Forms of Degree 2 (2011, methodology): “The book [15] by Eichler and Zagier gives a streamlined account of the construction of Saito-Kurokawa lifts via the theory of Jacobi forms.”
Note on twisted elliptic genus of K3 surface (2010, methodology): “We first introduce the standard notation in the theory of Jacobi forms [12]”
Distribution of mass of holomorphic cusp forms (2012, background): “cations connected with norms of automorphic forms restricted to certain submanifolds. For a holomorphic cuspidal Hecke eigenform g∈ S2k with kodd let Fg ∈ Sk+1(Sp4(Z)) be its Saito-Kurokawa lift (see [EZ]). Then Fg restricted to the diagonal is a modular form on (Γ\H) × 4 VALENTIN BLOMER, RIZWANUR K”
Elliptic Hypergeometry of Supersymmetric Dualities (2009, background): “[27] M. Eichler and D. Zagier, The Theory of Jacobi Forms, Progress in Math.”