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Special Values of Zeta-Functions for Proper Regular Arithmetic Surfaces


Siebel, Daniel A. (2019) Special Values of Zeta-Functions for Proper Regular Arithmetic Surfaces. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/YMHN-2T74.


We explicate Flach's and Morin's special value conjectures in [8] for proper regular arithmetic surfaces π : X → Spec Z and provide explicit formulas for the conjectural vanishing orders and leading Taylor coefficients of the associated arithmetic zeta-functions. In particular, we prove compatibility with the Birch and Swinnerton-Dyer conjecture, which has so far only been known for projective smooth X. Further, we derive a direct sum decomposition of Rπ*Z(n) into motivic degree components.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Special Values, Zeta-Functions, Arithmetic Surface
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Awards:Apostol Award for Excellence in Teaching in Mathematics, 2015.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Flach, Matthias
Thesis Committee:
  • Mantovan, Elena (chair)
  • Flach, Matthias
  • Graber, Thomas B.
  • Amir-Khosravi, Zavosh
Defense Date:9 November 2018
Record Number:CaltechTHESIS:11142018-032432585
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11273
Deposited By: Daniel Siebel
Deposited On:10 Dec 2018 22:13
Last Modified:04 Oct 2019 00:23

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