AN OVERVIEW OF ZETA FUNCTIONS ON HYPERSURFACES OVER FINITE FIELDS AND DWORK'S THEOREM

夏良忠連城2019-09-052014-7-242019-09-052014http://etds.lib.ntnu.edu.tw/cgi-bin/gs32/gsweb.cgi?o=dstdcdr&s=id=%22GN060040039S%22.&%22.id.&http://rportal.lib.ntnu.edu.tw:80/handle/20.500.12235/101703We study the Hasse Weil zeta function associated to a hypersurface of dimension n over finite field. The main goal is to give an overview of the proof of Dwork's Theorem. The main ingredients are p-adic analysis, linear algebra, and Weierstrass Preparation Theoremfinite fieldsp-adic numbersDwork's TheoremNewton polygonWeierstrass Preparation TheoremAN OVERVIEW OF ZETA FUNCTIONS ON HYPERSURFACES OVER FINITE FIELDS AND DWORK'S THEOREMAN OVERVIEW OF ZETA FUNCTIONS ON HYPERSURFACES OVER FINITE FIELDS AND DWORK'S THEOREM