## On a Cubic Shimura Integral for a Rank Two Symplectic Group |

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### Contents

Preliminaries | 8 |

The cubic GSp4xGL3 convolution | 18 |

Cubic metaplectic Hecke operators | 29 |

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2 other sections not shown

### Common terms and phrases

b(ac bd mod Bump and Hoffstein coefficients of z6n conjectured continuation and functional coprime cosets contribute Np5ap cosets contribute Np9/2ap cosets contribute zero cover of GL(n cover of GSp(4 cubic cover cubic metaplectic automorphic cubic reciprocity cubic theta function degree 4 Euler double cover double Dirichlet series dx2 dx3 dyl dy2 eigenfunction ep ap Euler product explicit explicitly form on GL(3 form on GSp(4 functional equation G Z[a Gauss sums GL(n half-integral weight forms Hecke operators Hoffstein BH2 L-functions Math maximal parabolic meromorphic continuation metaplectic automorphic form metaplectic cusp form metaplectic group minimal parabolic Eisenstein mod p2 modular form n-fold cover nln2 non-metaplectic P J These cosets parabolic Eisenstein series Proposition 1.1 Rankin-Selberg method Re(s Section Shimura Integral Shimura type Rankin-Selberg Shimura's techniques sum of coefficients Symplectic Group Theorem 5.1 type Rankin-Selberg integral Whittaker functions Whittaker-Fourier coefficients whole complex plane