Tonghai Yang

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In [17], a certain family of Siegel Eisenstein series of genus g and weight (g + 1)/2 was introduced. They have an odd functional equation and hence have a natural zero at their center of symmetry (s = 0). It was suggested that the derivatives at s = 0 of such series, which we will refer to as incoherent Eisenstein series, should have some connection with(More)
ignoring many important details and serious technical problems in the process. I apologize at the outset for the very speculative nature of the picture given here. I hope that, in spite of many imprecisions, the sketch will provide a context for a variety of particular cases where precise results have been obtained. Recent results on one of these, part of(More)
Every Hecke character of K satisfying (1.1) and (1.2) is actually a quadratic twist of a canonical Hecke character (see Section 2 for a precise description of these characters and which fields have them). Let L(s, χ) denote the Hecke L-function of χ, and Λ(s, χ) its completion; Λ(s, χ) satisfies the functional equation Λ(s, χ) = W (χ)Λ(2 − s, χ), where W(More)
We study the Faltings height pairing of arithmetic Heegner divisors and CM cycles on Shimura varieties associated to orthogonal groups. We compute the Archimedian contribution to the height pairing and derive a conjecture relating the total pairing to the central derivative of a Rankin L-function. We prove the conjecture in certain cases where the Shimura(More)
This function can be obtained, via analytic continuation, as a special value of an Eisenstein series E(τ, s) at s = 12 . In this note, we will give an arithmetic interpretation to Zagier’s Eisenstein series and its derivative at s = 12 , using Arakelov theory. Let M be the Deligne–Rapoport compactification of the moduli stack over Z of elliptic curves [DR].(More)