Derivatives of Eisenstein series and arithmetic geometry
| dc.creator | Kudla, Stephen S. | |
| dc.date | 2003-04-16 | |
| dc.date.accessioned | 2026-07-07T04:56:58Z | |
| dc.date.available | 2026-07-07T04:56:58Z | |
| dc.description | We describe connections between the Fourier coefficients of derivatives of Eisenstein series and invariants from the arithmetic geometry of the Shimura varieties $M$ associated to rational quadratic forms $(V,Q)$ of signature $(n,2)$. In the case $n=1$, we define generating series $\hatϕ_1(τ)$ for 1-cycles (resp. $\hatϕ_2(τ)$ for 0-cycles) on the arithmetic surface $\Cal M$ associated to a Shimura curve over $\Bbb Q$. These series are related to the second term in the Laurent expansion of an Eisenstein series of weight $\frac32$ and genus 1 (resp. genus 2) at the Siegel--Weil point, and these relations can be seen as examples of an `arithmetic' Siegel--Weil formula. Some partial results and conjectures for higher dimensional cases are also discussed. | |
| dc.identifier | https://arxiv.org/abs/math/0304234 | |
| dc.identifier | http://arxiv.org/abs/math/0304234 | |
| dc.identifier | Proceedings of the ICM, Beijing 2002, vol. 2, 173--184 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67115 | |
| dc.subject | Number Theory | |
| dc.subject | 14G40, 14G35, 11F30 | |
| dc.title | Derivatives of Eisenstein series and arithmetic geometry | |
| dc.type | text |