2020/04/12 by Yang Liu, Liu, Yang
Mathematics · Physics and Astronomy · #33C65 #46L87 #47A60 #58B34 #58Exx #58J40 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Random Matrices and Applications #math-ph #math.MP #math.QA #msc:33C65 #msc:46L87 #msc:47A60 #msc:58B34 #msc:58Exx #msc:58J40
paper · pdf · doi:10.48550/arxiv.2004.05714
43 pages
arxiv created 2020/04/12 · openalex publication_date 2020/04/12 · arxiv updated 2020/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a technical problem arising from the spectral geometry of noncommutative tori: the small time heat trace asymptotic associated to a general second order elliptic operator. We extend the rearrangement operators in the conformal case to the general setting using hypergeometric integrals over Grassmannians. The main result is the explicit formula of the second heat coefficient in terms of the coefficients. When specializing to examples in conformal case, we not only recover results in previous works but also obtain some extra functional relations whose validation provides experimental support to the main results. At last, we verify the relations based on combinatorial properties derived from the hypergeometric features.