Cyclotomic classes
WebDec 1, 1985 · In the first part of the paper we show how to construct real cyclotomic fields with large class numbers. If the GRH holds then the class number hp+ of the p th real … WebNov 25, 2016 · Kummer's class number formula gives for the first factor $ 37 $ and the second factor can be determined to $ 1 $ by the Minkowski bound in the real …
Cyclotomic classes
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WebThe cyclotomic fields are among the most intensively studied classes of number fields. Yet their class numbers remain quite mysterious. Surprisingly, for cyclotomic fields of prime conductor, the class number has only been determined up to conductor 67, and no further cyclotomic fields of prime conductor have had their class numbers deter- WebJun 4, 2024 · This paper contributes to constructing two classes of quantum synchronizable codes by the cyclotomic classes of order two over $\mathbb{Z}_{2q}$, whose synchronization capabilities can reach the upper bound under certain conditions. Moreover, the quantum synchronizable codes possess good error-correcting capability towards bit …
WebFeb 15, 2002 · ldenotes the class group of the ring of integers of the real cyclotomic eld Q( l + 1 l). Its order, theclass numberof Q( l 1 l), is denoted byh l. The quotient groupCl lis rather well understood. Already in the 19th century, E.E. Kummer [12], [13] computed the orders of the groupsCl lforl<100. Webcyclotomic classes is described in Section 3. 2 DSS and quadratic residues Let D = {x 1, x 2,...,x k} be a (v,k,λ) difference set (cf. [1], [2], [7]), that is, a subset of k residues modulo v such that every positive residue modulo v occurs exactly λ times in the multi-set of differences {x i −x
WebA partition of is a family of sets, satisfying If there exist a subgroup of and of , satisfying ,, then the are called to be classical cyclotomic classes with order if is a prime number, and generalized cyclotomic classes with order if is a composite number. The (generalized) cyclotomic numbers with order are defined as. Lemma 4.
The cyclotomic polynomials are monic polynomials with integer coefficients that are irreducible over the field of the rational numbers. Except for n equal to 1 or 2, they are palindromics of even degree. The degree of , or in other words the number of nth primitive roots of unity, is , where is Euler's totient function.
Web20 hours ago · I defined the arithmetic operators for a S4 class cyclotomic: cyclotomic_arith_cyclotomic <- function(e1, e2) { switch( .Generic, "+" = sumCyc(e1, e2), "-" = su... flying horse pubWebMar 26, 2024 · An important theorem that describes the structure of the class groups of cyclotomic fields in terms of $ p $-adic $ L $-functions has been proved by B. Mazur … flying horse north mapWebThe class number of cyclotomic rings of integers is the product of two factors and one factor is relatively simple to compute. For the 23 rd cyclotomic ring of integers, the first … flying horse pub boughton leesWebMay 16, 2006 · In this talk we discuss the problem of calculating class numbers of cyclotomic fields. This is a computational problems that, even using the fastest … flying horse pub clophillWebLinear complexity is an important criterion to characterize the unpredictability of pseudo-random sequences, and large linear complexity corresponds to high cryptographic strength. Pseudo-random Sequences with a large linear complexity property are of importance in many domains. In this paper, based on the theory of inverse Gray mapping, two classes … flying horse nzWeb1. Cyclotomic fields 3 2. An outline of class field theory 4 3. Relative class number formula and Stickelberger’s theorem 6 4. Basic properties of Gauss sum 7 5. Prime factorization of Gauss sum 10 6. A consequence of the Kummer–Vandiver conjecture 14 7. Kummer theory 16 8. Cyclicity theorem for F0 = Q[µp] 17 9. Proof of the cyclicity ... flying horse pub boughton aluphWebNov 1, 2016 · In this paper, 2-adic complexity of two classes of generalized cyclotomic binary sequences is investigated. The sequences in the first class have period p (p+4), and their 2-adic complexity attains ... View via Publisher Save to Library Create Alert Cite 11 Citations Citation Type More Filters green lumbar christmas pillow