Computing Zeta Functions in Families of Ca, b
نویسندگان
چکیده
We apply deformation theory to compute zeta functions in a family of Ca,b curves over a finite field of small characteristic. The method combines Denef and Vercauteren’s extension of Kedlaya’s algorithm to Ca,b curves with Hubrechts’ recent work on point counting on hyperelliptic curves using deformation. As a result, it is now possible to generate Ca,b curves suitable for use in cryptography in a matter of minutes.
منابع مشابه
Computing zeta functions in families of Ca,b curves using deformation
We apply deformation theory to compute zeta functions in a family of Ca,b curves over a finite field of small characteristic. The method combines Denef and Vercauteren’s extension of Kedlaya’s algorithm to Ca,b curves with Hubrechts’ recent work on point counting on hyperelliptic curves using deformation. As a result, it is now possible to generate Ca,b curves suitable for use in cryptography i...
متن کاملComparison of Three Soft Computing Methods in Estimating Apparent Shear Stress in Compound Channels
Apparent shear stress acting on a vertical interface between the main channel and floodplain in a compound channel serves to quantify the momentum transfer between sub sections of this cross section. In this study, three soft computing methods are used to simulate apparent shear stress in prismatic compound channels. The Genetic Algorithm Artificial neural network (GAA), Genetic Programming (GP...
متن کاملGeometric Studies on Inequalities of Harmonic Functions in a Complex Field Based on ξ-Generalized Hurwitz-Lerch Zeta Function
Authors, define and establish a new subclass of harmonic regular schlicht functions (HSF) in the open unit disc through the use of the extended generalized Noor-type integral operator associated with the ξ-generalized Hurwitz-Lerch Zeta function (GHLZF). Furthermore, some geometric properties of this subclass are also studied.
متن کاملAsymptotic Properties of Dedekind Zeta Functions in Families of Number Fields
The main goal of this paper is to prove a formula that expresses the limit behaviour of Dedekind zeta functions for Re s > 1/2 in families of number fields, assuming that the Generalized Riemann Hypothesis holds. This result can be viewed as a generalization of the Brauer–Siegel theorem. As an application we obtain a limit formula for Euler–Kronecker constants in families of number fields.
متن کاملSome properties and results involving the zeta and associated functions
In this research-cum-expository article, we aim at presenting a systematic account of some recent developments involving the Riemann Zeta function ζ(s), the Hurwitz (or generalized) Zeta function ζ(s, a), and the Hurwitz-Lerch Zeta function Φ(z, s, a) as well as its various interesting extensions and generalizations. In particular, we begin by looking into the problems associated with the evalu...
متن کامل