We present two algorithms to compute the endomorphism ring of an ordinary elliptic curve E defined over a finite field Fq . Under suitable heuristic assumptions, both have subexponential complexity. We bound the complexity of the first algorithm in terms of log q , while our bound for the second algorithm depends primarily on log |DE |, where DE is the discriminant of the order isomorphic to En...

In this article we consider the zeta regularized determinant of Laplace-type operators on the generalized cone. For arbitrary self-adjoint extensions of a matrix of singular ordinary differential operators modelled on the generalized cone, a closed expression for the determinant is given. The result involves a determinant of an endomorphism of a finite-dimensional vector space, the endomorphism...

We study the scaling function of a C1+h expanding circle endomorphism. We find necessary and sufficient conditions for a Hölder continuous function on the dual symbolic space to be realized as the scaling function of a C1+h expanding circle endomorphism. We further represent the Teichmüller space of C1+h expanding circle endomorphisms by the space of Hölder continuous functions on the dual symb...

for all x, y£L. It is easily shown that every join-endomorphism is an isotone correspondence (i.e. x^y implies ®x=i 8y). It is also easy to see that the set / of antecedents of 0 under any join-endomorphism is an ideal. (For these and other facts used in the sequel we refer to the textbook of G. Birkhoff, Lattice theory, rev. ed., New York, 1948, henceforth cited as LT.) G. Birkhoff states in L...

A fixed point theorem is proved for inverse transducers, leading to an automatatheoretic proof of the fixed point subgroup of an endomorphism of a finitely generated virtually free group being finitely generated. If the endomorphism is uniformly continuous for the hyperbolic metric, it is proved that the set of regular fixed points in the hyperbolic boundary has finitely many orbits under the a...

Comparing the bounded derived categories of an algebra and endomorphism a given support {\tau}-tilting module, we find relation between dimensions module.

In 2001, an open question that was posed by Blyth, Silva and Varlet in [2] is the following: for an Ockham algebra L determine the congruences on L that are kernels of endomorphisms on L. Whereas a general solution to this is stll an open problem, there has been some progress in investigating kernels of endomorphisms in various lattice-ordered algebras. In this connection, an algebra A is said ...