Group arithmetic inC3,5curves

Arithmetic Rigidity and Units in Group Rings

For any finite group G the group U(Z[G]) of units in the integral group ring Z[G] is an arithmetic group in a reductive algebraic group, namely the Zariski closure of SL1(Q[G]). In particular, the isomorphism type of the Q-algebra Q[G] determines the commensurability class of U(Z[G]); we show that, to a large extent, the converse is true. In fact, subject to a certain restriction on the Q-repre...

Fast Jacobian Group Arithmetic on CabCurves

The goal of this paper is to describe a practical and eecient algorithm for computing in the Jacobian of a large class of algebraic curves over a nite eld. For elliptic and hyperelliptic curves, there exists an algorithm for performing Jaco-bian group arithmetic in O(g 2) operations in the base eld, where g is the genus of a curve. The main problem in this paper is whether there exists a method...

ARITHMETIC-BASED FUZZY CONTROL

Fuzzy control is one of the most important parts of fuzzy theory for which several approaches exist. Mamdani uses $alpha$-cuts and builds the union of the membership functions which is called the aggregated consequence function. The resulting function is the starting point of the defuzzification process. In this article, we define a more natural way to calculate the aggregated consequence funct...

Arithmetic Aggregation Operators for Interval-valued Intuitionistic Linguistic Variables and Application to Multi-attribute Group Decision Making

The intuitionistic linguistic set (ILS) is an extension of linguisitc variable. To overcome the drawback of using single real number to represent membership degree and non-membership degree for ILS, the concept of interval-valued intuitionistic linguistic set (IVILS) is introduced through representing the membership degree and non-membership degree with intervals for ILS in this paper. The oper...

An Exceptional Arithmetic Group and Its Eisenstein Series