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Effective bounds for Faltings’s delta function

Jay JorgensonJürg Kramer — 2014

Annales de la faculté des sciences de Toulouse Mathématiques

In his seminal paper on arithmetic surfaces Faltings introduced a new invariant associated to compact Riemann surfaces X , nowadays called Faltings’s delta function and here denoted by δ Fal ( X ) . For a given compact Riemann surface X of genus g X = g , the invariant δ Fal ( X ) is roughly given as minus the logarithm of the distance with respect to the Weil-Petersson metric of the point in the moduli space g of genus g curves determined by X to its boundary g . In this paper we begin by revisiting a formula derived in [14],...

Unipotent vector bundles and higher-order non-holomorphic Eisenstein series

Jay JorgensonCormac O’Sullivan — 2008

Journal de Théorie des Nombres de Bordeaux

Higher-order non-holomorphic Eisenstein series associated to a Fuchsian group Γ are defined by twisting the series expansion for classical non-holomorphic Eisenstein series by powers of modular symbols. Their functional identities include multiplicative and additive factors, making them distinct from classical Eisenstein series. In this article we prove the meromorphic continuation of these series and establish their functional equations which relate values at s and 1 - s . In addition, we construct...

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