Choice Mappings of Certain Classes of Finite Sets.
Cholesky factorizations of matrices associated with -order recurrent sequences.
Chowla's conjecture
Chromatic roots of a ring of four cliques.
CHRONIQUE (vol. 1, Fasc. 2.)
Cinq nombres dont les sommes deux à deux sont des carrés
Cipolla pseudoprimes.
Circles passing through five or more integer points
We find an improvement to Huxley and Konyagin’s current lower bound for the number of circles passing through five integer points. We conjecture that the improved lower bound is the asymptotic formula for the number of circles passing through five integer points. We generalise the result to circles passing through more than five integer points, giving the main theorem in terms of cyclic polygons with m integer point vertices. Theorem. Let m ≥ 4 be a fixed integer. Let be the number of cyclic polygons...
Circulants and the factorization of the Fibonacci–like numbers
Several authors gave various factorizations of the Fibonacci and Lucas numbers. The relations are derived with the help of connections between determinants of tridiagonal matrices and the Fibonacci and Lucas numbers using the Chebyshev polynomials. In this paper some results on factorizations of the Fibonacci–like numbers and their squares are given. We find the factorizations using the circulant matrices, their determinants and eigenvalues.
Circular units of real abelian fields with four ramified primes
In this paper we study the groups of circular numbers and circular units in Sinnott’s sense in real abelian fields with exactly four ramified primes under certain conditions. More specifically, we construct -bases for them in five special infinite families of cases. We also derive some results about the corresponding module of relations (in one family of cases, we show that the module of Ennola relations is cyclic). The paper is based upon the thesis [6], which builds upon the results of the paper...
Čísla a početní výkony [Book]
Class 2 Galois representations of Kummer type.
Class fields of abelian extensions of Q.
Class fields towers of imaginary quadratic fields.
Class group of a cyclotomic -extension
Class Group Rank Relations in Zl-Extensions.
Class groups and general linear group cohomology for a ring of algebraic integers.
Class groups of abelian fields, and the main conjecture
This first part of this paper gives a proof of the main conjecture of Iwasawa theory for abelian base fields, including the case , by Kolyvagin’s method of Euler systems. On the way, one obtains a general result on local units modulo circular units. This is then used to deduce theorems on the order of -parts of -class groups of abelian number fields: first for relative class groups of real fields (again including the case ). As a consequence, a generalization of the Gras conjecture is stated...
Class groups of global fields.
Class groups under relative quadratic extensions