منابع مشابه
Cyclotomy and Endomotives
We compare two different models of noncommutative geometry of the cyclotomic tower, both based on an arithmetic algebra of functions of roots of unity and an action by endomorphisms, the first based on the Bost-Connes (BC) quantum statistical mechanical system and the second on the Habiro ring, where the Habiro functions have, in addition to evaluations at roots of unity, also full Taylor expan...
متن کاملNew D-optimal designs via cyclotomy and generalised cyclotomy
D-optimal designs are n x n ±l-matrices where n == 2 mod 4 with maximum determinant. D-optimal designs obtained via circulant matrices are equivalent to 2-{ v; kl i k2 i k1 + k2 ~(v 1)} supplementary difference sets, where v = ~. We use cyclotomy to construct D-optimal designs, where v is a prime. We give a generalisation of cyclotomy and extend the cyclotomic techniques which enables use to fi...
متن کاملCyclotomy and Delta Units
In this paper we examine cyclic cubic, quartic, and quintic number fields of prime conductor p containing units that bear a special relationship to the classical Gaussian periods: n¡ nj+x + c is a unit for periods r\¡ and c e Z.
متن کاملCyclotomy Primality Proving
Two rational primes p, q are called dual elliptic if there is an elliptic curve E mod p with q points. They were introduced as an interesting means for combining the strengths of the elliptic curve and cyclotomy primality proving algorithms. By extending to elliptic curves some notions of galois theory of rings used in the cyclotomy primality tests, one obtains a new algorithm which has heurist...
متن کاملCovering arrays from cyclotomy
For a prime power q ≡ 1 (mod v), the q × q cyclotomic matrix, whose entries are the discrete logarithmsmodulo v of the entries in the addition table of Fq , has been shown using character theoretic arguments to produce an ε-biased array, provided that q is large enough as a function of v and ε. A suitable choice of ε ensures that the array is a covering array of strength t when q > t2v4t . On t...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1982
ISSN: 0022-314X
DOI: 10.1016/0022-314x(82)90058-0