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

Voir la notice de l'article provenant de la source Annals of Mathematics website

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 
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Zhiwei Yun; Wei Zhang. Shtukas and the Taylor expansion of $L$-functions. Annals of mathematics, Tome 186 (2017) no. 3, pp. 767-911. doi : 10.4007/annals.2017.186.3.2. http://geodesic.mathdoc.fr/articles/10.4007/annals.2017.186.3.2/

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