Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp012n49t486r
 Title: Harmonic Analysis on Local Systems on Graphs -- Towards a Gross-Zagier Formula on CM-cycles over Shimura Curves Authors: Wen, Boya Advisors: Zhang, Shou-Wu Contributors: Mathematics Department Keywords: Green's functionGross-Zagier formulaHeight pairingLocal systems on Graphs Subjects: Mathematics Issue Date: 2022 Publisher: Princeton, NJ : Princeton University Abstract: In Part I of the thesis, we study harmonic analysis on local systems over graphs, and construct Green's functions explicitly. In Part II, we apply the results in Part I towards a Gross-Zagier formula for CM cycles over Shimura curves, which connects the global height pairing of special cycles in Kuga varieties over Shimura curves with the derivatives of the $L$-functions associated to weight-$2k$ modular forms. More precisely, we present a suitable choice of integral model of the CM cycles, and compute local intersections at primes where the quaternion algebra associated with the Shimura curve ramifies. URI: http://arks.princeton.edu/ark:/88435/dsp012n49t486r Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: catalog.princeton.edu Type of Material: Academic dissertations (Ph.D.) Language: en Appears in Collections: Mathematics