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- Stephen S. Kudla, Michael, Tonghai Yang
- 1999

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)

- Tonghai Yang, Tonghai Yang
- 2004

Let S and T be two positive definite integral matrices of rank m and n respectively. It is an ancient but still very challenging problem to determine how many times S can represent T , i.e., the number of integral matrices X with XSX = T . However, Siegel proved in his celebrated paper ([Si1]) that certain weighted averages of these numbers over the genus… (More)

- Tonghai Yang
- 2008

In this paper, we prove an explicit arithmetic intersection formula between arithmetic Hirzebruch-Zagier divisors and arithmetic CM cycles in a Hilbert modular surface over Z. As applications, we obtain the first ‘non-abelian’ Chowla-Selberg formula, which is a special case of Colmez’s conjecture; an explicit arithmetic intersection formula between… (More)

- STEPHEN S. KUDLA, Tonghai Yang
- 2003

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)

- Stephen S. Kudla, Michael Rapoport, Tonghai Yang
- 2001

In a series of papers, [25], [30], [28], [29], [31], [26], we showed that certain quantities from the arithmetic geometry of Shimura varieties associated to orthogonal groups occur in the Fourier coefficients of the derivative of suitable Siegel-Eisenstein series. It was essential in these examples that this derivative was the second term in the Laurent… (More)

- JAN HENDRIK, Tonghai Yang
- 2008

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)

- Tonghai Yang, Tonghai Yang
- 2003

In this paper, we associate canonically to every imaginary quadratic field K = Q(√−D) one or two isogenous classes of CM (complex multiplication) abelian varieties over K, depending on whether D is odd or even (D 6= 4). These abelian varieties are characterized as of smallest dimension and smallest conductor, and such that the abelian varieties themselves… (More)

- Tonghai Yang, Stephen Kudla
- 2004

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)