Higher dimensional adeles, meanperiodicity and zeta functions of arithmetic surfacesTools Oliver, Thomas David (2014) Higher dimensional adeles, meanperiodicity and zeta functions of arithmetic surfaces. PhD thesis, University of Nottingham.
AbstractThis thesis is concerned with the analytic properties of arithmetic zeta functions, which remain largely conjectural at the time of writing. We will focus primarily on the most basic amongst them  meromorphic continuation and functional equation. Our weapon of choice is the socalled “meanperiodicity correspondence”, which provides a passage between nicely behaved arithmetic schemes and meanperiodic functions in certain functional spaces. In what follows, there are two major themes.
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