L${L}$‐functions of Kloosterman sheaves
Copyright policy )L${L}$‐functions of Kloosterman sheaves
AbstractIn this article, we study a family of motives associated with the symmetric power of Kloosterman sheaves constructed by Fresán, Sabbah, and Yu. They demonstrated that for , the ‐functions of extend meromorphically to and satisfy the functional equations conjectured by Broadhurst and Roberts. Our work aims to extend these results to the ‐functions of some of the motives , with , as well as other related two‐dimensional motives. In particular, we prove several conjectures of Evans type, which relate moments of Kloosterman sheaves and Fourier coefficients of modular forms.
- Humboldt-Universität zu Berlin Germany
ddc:510, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Fourier coefficients of automorphic forms, Mathematics - Algebraic Geometry, Mathematics - Number Theory, Galois representations, FOS: Mathematics, 510 Mathematik, Number Theory (math.NT), Gauss and Kloosterman sums; generalizations, Algebraic Geometry (math.AG)
ddc:510, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Fourier coefficients of automorphic forms, Mathematics - Algebraic Geometry, Mathematics - Number Theory, Galois representations, FOS: Mathematics, 510 Mathematik, Number Theory (math.NT), Gauss and Kloosterman sums; generalizations, Algebraic Geometry (math.AG)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).1 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!