## Abstract

Let Z be the quotient of the Siegel modular threefold A^{sa}(2, 4, 8) which has been studied by van Geemen and Nygaard. They gave an implication that some 6-tuple F_{Z} of theta constants which is in turn known to be a Klingen type Eisenstein series of weight 3 should be related to a holomorphic differential (2, 0)-form on Z. The variety Z is birationally equivalent to the tangent cone of Fermat quartic surface in the title. In this paper we first compute the L-function of two smooth resolutions of Z. One of these, denoted by W, is a kind of Igusa compactification such that the boundary ∂W is a strictly normal crossing divisor. The main part of the L-function is described by some elliptic newform g of weight 3. Then we construct an automorphic representation π of GSp_{2}(A) related to g and an explicit vector E_{Z} sits inside π which creates a vector valued (non-cuspidal) Siegel modular form of weight (3, 1) so that F_{Z} coincides with E_{Z} in H^{2,0}(∂W) under the Poincaré residue map and various identifications of cohomologies.

Original language | English |
---|---|

Pages (from-to) | 585-630 |

Number of pages | 46 |

Journal | Advances in Theoretical and Mathematical Physics |

Volume | 21 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2017 Jan 1 |

## ASJC Scopus subject areas

- Mathematics(all)
- Physics and Astronomy(all)