Shtukas and the Taylor expansion of L-functions (II)
成果类型：
Article
署名作者：
Yun, Zhiwei; Zhang, Wei
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2019.189.2.2
发表日期：
2019
页码：
393-526
关键词：
摘要：
For arithmetic applications, we extend and refine our previously published results to allow ramifications in a minimal way. Starting with a possibly ramified quadratic extension F'/F of function fields over a finite field in odd characteristic, and a finite set of places Sigma of F that are unramified in F', we define a collection of Heegner-Drinfeld cycles on the moduli stack of PGL(2)-Shtukas with r-modifications and Iwahori level structures at places of Sigma. For a cuspidal automorphic representation pi of PGL(2) (A(F)) with square-free level Sigma, and r is an element of Z(>= 0) whose parity matches the root number of pi(F'), we prove a series of identities between (1) the product of the central derivatives of the normalized L-functions L-(a) (pi, 1/2) L(r-a) (pi circle times eta, 1/2), where eta is the quadratic idele class character attached to F'/F, and 0 <= a <= r; (2) the self intersection number of a linear combination of Heegner-Drinfeld cycles. In particular, we can now obtain global L-functions with odd vanishing orders. These identities are function-field analogues of the formulae of Waldspurger and Gross-Zagier for higher derivatives of L-functions.