Shtukas and the Taylor expansion of \(L\)-functions

DOI10.4007/annals.2017.186.3.2zbMath1385.11032arXiv1512.02683OpenAlexW2962689222WikidataQ101094189 ScholiaQ101094189MaRDI QIDQ1679187

Zhiwei Yun, Wei Zhang

Publication date: 8 November 2017

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.02683

zbMATH Keywords

\(L\)-functionsGross-Zagier formulaDrinfeld ShtukasWaldspurger formula

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Modular and Shimura varieties (14G35) Vector bundles on curves and their moduli (14H60) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items (15)

Eichler cohomology and zeros of polynomials associated to derivatives of \(L\)-functions ⋮ An intersection formula for CM cycles on Lubin-Tate spaces ⋮ Isolation of the cuspidal spectrum: the function field case ⋮ The Gross-Zagier-Zhang formula over function fields ⋮ From sum of two squares to arithmetic Siegel–Weil formulas ⋮ Recent progress on the Tate conjecture ⋮ Cohomological \(\chi\)-independence for moduli of one-dimensional sheaves and moduli of Higgs bundles ⋮ Higher Siegel-Weil formula for unitary groups: the non-singular terms ⋮ Arithmetic Siegel-Weil formula on \(X_{0}(N)\) ⋮ Shtukas and the Taylor expansion of \(L\)-functions. II ⋮ A Gross-Kohnen-Zagier formula for Heegner-Drinfeld cycles ⋮ Product formulas for periods of CM abelian varieties and the function field analog ⋮ The arithmetic fundamental lemma: an update ⋮ Super-positivity of a family of \(L\)-functions in the level aspect ⋮ Tate cycles on some quaternionic Shimura varieties mod \(p\)

Cites Work

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