Geometric invariants for real quadratic fields

• 成果类型: Article
• 署名作者: Duke, W.; Imamoglu, O.; Toth, A.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2016.184.3.8
• 发表日期: 2016
• 页码: 949-990
• 关键词: fourier coefficients; modular-forms; CLOSED GEODESICS; cycle integrals; l-series; weight; computation; VALUES; bounds; sums

摘要

To an ideal class of a real quadratic field eve associate a certain surface. This surface, which is a new geometric invariant, has the usual modular closed geodesic as its boundary. Furthermore, its area, is determined by the length of an associated backward continued fraction. We study the distribution properties of this surface on average over a genus. In the process we give an extension and refinement of the Katok-Sarnak formula.