Geodesic
Shtukas and the Taylor expansion of $L$-functions
Zhiwei Yun1; Wei Zhang2
1Yale University, New Haven, CT
2Columbia University, New York, NY
Annals of mathematics, Volume 186 (2017) no. 3, pp. 767-911

See the original article notice from the Annals of Mathematics website source

MR Zbl

We define the Heegner–Drinfeld cycle on the moduli stack of Drinfeld Shtukas of rank two with $r$-modifications for an even integer $r$. We prove an identity between (1) the $r$-th central derivative of the quadratic base change $L$-function associated to an everywhere unramified cuspidal automorphic representation $\pi$ of $\mathrm{PGL}_{2}$, and (2)~the self-intersection number of the $\pi$-isotypic component of the Heegner–Drinfeld cycle. This identity can be viewed as a function-field analog of the Waldspurger and Gross–Zagier formula for higher derivatives of $L$-functions.

DOI: 10.4007/annals.2017.186.3.2

Zhiwei Yun  1 ; Wei Zhang  2

1 Yale University, New Haven, CT
2 Columbia University, New York, NY 
Zhiwei Yun; Wei Zhang. Shtukas and the Taylor expansion of $L$-functions. Annals of mathematics, Volume 186 (2017) no. 3, pp. 767-911. doi: 10.4007/annals.2017.186.3.2
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     title = {Shtukas and the {Taylor} expansion of $L$-functions},
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     pages = {767--911},
     year = {2017},
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