Based on Furusawa’s theory [7], we present an integral representation for the L-function L(s, π× τ), where π is a cuspidal automorphic representation on GSp4 related to a holomorphic Siegel modular form, and where τ is an arbitrary cuspidal automorphic representation on GL2. As an application, a special value result for this L-function in the spirit of Deligne’s conjecture is proved.

In this paper, we study the period map of a certain one-parameter family of quartic K3 surfaces with an S5-action. We construct automorphic forms on the period domain as the pull-backs of theta constants of genus 2 by a modular embedding. Using these automorphic forms, we give an explicit presentation of the inverse period map.

2 Modular forms and Automorphic forms 2 2.1 Modular Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 The Adele group of GL2 over Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Automorphic Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Hecke act...

The automorphic A-chromatic index of a graph Γ is the minimum integer m for which Γ has a proper edge-coloring with m colors which is preserved by a given subgroup A of the full automorphism group of Γ. We compute the automorphic A-chromatic index of each generalized Petersen graph when A is the full automorphism group.

We show that the irregular connection on Gm constructed by Frenkel-Gross ([FG]) and the one constructed by Heinloth-Ngô-Yun ([HNY]) are the same, which confirms the Conjecture 2.14 of [HNY]. The proof is simple, modulo the big machinery of quantization of Hitchin’s integrable systems as developed by Beilinson-Drinfeld ([BD]). The idea is as follows. Let E be the irregular connection on Gm as co...

The elliptic genus (EG) of a compact complex manifold was introduced as a holomorphic Euler characteristic of some formal power series with vector bundle coefficients. EG is an automorphic form in two variables only if the manifold is a Calabi–Yau manifold. In physics such a function appears as the partition function of N = 2 superconformal field theories. In these notes we define the modified ...

The Holy Quran was descended from Almighty Allah to the Holy Prophet (AS) about the last 14 centuries and there has been a time interval between descent of the Quran and its existing readers and commentators. This Question is posed whether this time interval between descent of the Quran and commentator will effect on verses understanding and their commentary or not? As one of commentary princip...

We present a level raising result for families of p-adic automorphic forms for a definite quaternion algebra D over Q. The main theorem is an analogue of a theorem for classical automorphic forms due to Diamond and Taylor. One of the ingredients in the proof of Diamond and Taylor’s theorem (which also played a role in earlier work of Taylor) is the definition of a suitable pairing on the space ...

We show how the weight of automorphic forms is related to the holomorphic positive and negative line bundles. Then, from the relation of holomorphic vector bundles and the existence of Yang-Mills connection on the stable bundle , we discuss how the weight of automorphic forms can be associated with the transition function of the Yang-Mills connection.

We give in this work some sufficient conditions for the existence and uniqueness of almost automorphic (mild) solutions to some classes of partial evolution equations. Then we use our abstract results to discuss the existence and uniqueness of almost automorphic solutions to some partial differential equations. c © 2006 Elsevier Ltd. All rights reserved.