scholarly journals On the zeta functions of supersingular curves

2018 ◽  
Vol 54 ◽  
pp. 65-79 ◽  
Author(s):  
Gary McGuire ◽  
Emrah Sercan Yılmaz
Keyword(s):  
Zeta Functions ◽  
Supersingular Curves

scholarly journals Zeta Functions of Supersingular Curves of Genus 2

2007 ◽  
Vol 59 (2) ◽  
pp. 372-392 ◽  
Author(s):  
Daniel Maisner ◽  
Enric Nart
Keyword(s):  
Finite Field ◽  
Zeta Function ◽  
Zeta Functions ◽  
Abelian Surfaces ◽  
Genus 2 ◽  
Characteristic 2 ◽  
Supersingular Curves

AbstractWe determine which isogeny classes of supersingular abelian surfaces over a finite field k of characteristic 2 contain jacobians. We deal with this problem in a direct way by computing explicitly the zeta function of all supersingular curves of genus 2. Our procedure is constructive, so that we are able to exhibit curves with prescribed zeta function and find formulas for the number of curves, up to k-isomorphism, leading to the same zeta function.

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