The finite upper half planes over finite fields and rings are finite analogues of the PoincarΓ© upper half plane. The general linear group G acts transitively on the finite upper half plane. Let K denote the stabilizer of a point. In the case of fields, it is well-known that the pair of (G, K) is a G
Cyclotomic schemes over finite rings
β Scribed by R.W. Goldbach; H.L. Claasen
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 818 KB
- Volume
- 3
- Category
- Article
- ISSN
- 0019-3577
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
The aim of this note is to show that the (well-known) factorization of the 2 nΟ©1 th cyclotomic polynomial x 2 n Ο© 1 over GF(q) with q Ο΅ 1 (mod 4) can be used to prove the (more complicated) factorization of this polynomial over GF(q) with q Ο΅ 3 (mod 4).
Convolution algorithms for polynomial multiplication are well known, as is the use of Residue Number Systems and the Chinese Remainder Theorem. This paper discusses how these techniques may be used to perform polynomial arithmetic over very large rings or finite fields. The algorithm is practical an
Given a finite commutative ring with identity A, define c(A, n, R) as the minimum cardinality of a subset H of A n which satisfies the following property: every element in A n differs in at most R coordinates from a multiple of an element in H. In this work, we determine the numbers c(Z m , n, 0) fo