Derived categories and the analytic approach to general reciprocity laws. II.
Diamètres transfinis et problème de Favard
Tout entier algébrique irrationnel a deux conjugués éloignés d’au moins .
Die irreduziblen Zahlen des Bereichs Z [...-5].
Digital expansions in real algebraic quadratic fields.
Discrete self-similar multifractals with examples from algebraic number theory
Discriminants of Chebyshev radical extensions
Let be any integer and fix an odd prime . Let denote the -fold composition of the Chebyshev polynomial of degree shifted by . If this polynomial is irreducible, let , where is a root of . We use a theorem of Dedekind in conjunction with previous results of the author to give conditions on that ensure is monogenic. For other values of , we apply a result of Guàrdia, Montes, and Nart to obtain a formula for the discriminant of and compute an integral basis for the ring of integers...
Divisibility sequences and powers of algebraic integers.
Division-ample sets and the Diophantine problem for rings of integers
We prove that Hilbert’s Tenth Problem for a ring of integers in a number field has a negative answer if satisfies two arithmetical conditions (existence of a so-called division-ample set of integers and of an elliptic curve of rank one over ). We relate division-ample sets to arithmetic of abelian varieties.
Divisors in a Dedekind domain