In mathematics, Dirichlet's unit theorem is a basic result in algebraic number theory due to Peter Gustav Lejeune Dirichlet. It determines the rank of...

Lejeune Dirichlet's work was what led him to his later study of algebraic number fields and ideals. In 1863, he published Lejeune Dirichlet's lectures...

arithmetic progressions Dirichlet's approximation theorem Dirichlet's unit theorem Dirichlet conditions Dirichlet boundary condition Dirichlet's principle Pigeonhole...

argument, in the proof of a theorem in diophantine approximation, later named after him Dirichlet's approximation theorem. He published important contributions...

rank 1 (i.e. when the unit group modulo its torsion subgroup is infinite cyclic). Dirichlet's unit theorem shows that the unit group has rank 1 exactly...

multiplicative group containing the units of R. Dirichlet's unit theorem holds for S-units: the group of S-units is finitely generated, with rank (maximal...

a unit, and so are its powers, so Z[√3] has infinitely many units. More generally, for the ring of integers R in a number field F, Dirichlet's unit theorem...

because Ki then has units of infinite order by Dirichlet's unit theorem. The quantitative hypothesis of the standard Brauer–Siegel theorem is that if Di is...

theory) Dirichlet's unit theorem (algebraic number theory) Equidistribution theorem (ergodic theory) Erdős–Kac theorem (number theory) Euclid's theorem (number...

group Dirichlet's unit theorem Discriminant of an algebraic number field Ramification (mathematics) Root of unity Gaussian period Fermat's Last Theorem Class...

commonly called Dirichlet's box principle or Dirichlet's drawer principle after an 1834 treatment of the principle by Peter Gustav Lejeune Dirichlet under the...

number field is very similar. In the general case, by Dirichlet's unit theorem, the group of units in the ring of integers of K is infinite. One can nevertheless...

totally real subfield of K mentioned above. This follows from Dirichlet's unit theorem. The simplest, and motivating, example of a CM-field is an imaginary...

{\displaystyle [K:\mathbb {Q} ]=r+2s.} Remark. The Unit Theorem generalises Dirichlet's Unit Theorem. To see this, let K {\displaystyle K} be a number...

mathematics, Shintani's unit theorem introduced by Shintani (1976, proposition 4) is a refinement of Dirichlet's unit theorem and states that a subgroup...

conjectured to be PPP complete. Danzer set Pick's theorem Dirichlet's unit theorem Minkowski's second theorem Ehrhart's volume conjecture Olds, C. D.; Lax...

with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic progressions...

x+y{\sqrt {n}}} is a unit with norm 1 in Z [ n ] {\displaystyle \mathbb {Z} [{\sqrt {n}}]} . Dirichlet's unit theorem, that all units of Z [ n ] {\displaystyle...

In mathematical analysis, Fubini's theorem characterizes the conditions under which it is possible to compute a double integral by using an iterated integral...

the study of the Dirichlet's problem were taken by Karl Friedrich Gauss, William Thomson (Lord Kelvin) and Peter Gustav Lejeune Dirichlet, after whom the...

bagpipes Regulator (mathematics), a positive real number used in Dirichlet's unit theorem Regulator (biology), an animal that is able to maintain a constant...

rational root theorem for the case of a monic polynomial. Gaussian integer Eisenstein integer Root of unity Dirichlet's unit theorem Fundamental units Marcus...

ideals into prime ideals. The units of a ring of integers OK is a finitely generated abelian group by Dirichlet's unit theorem. The torsion subgroup consists...

is due to Dirichlet (in 1850), and has become classical. It requires three main lemmas: the quadratic reciprocity law, Dirichlet's theorem on arithmetic...

uniformization theorem states that every simply connected Riemann surface is conformally equivalent to one of three Riemann surfaces: the open unit disk, the...

includes the modulus. In many contexts (such as in the proof of Dirichlet's theorem) the modulus is fixed. In other contexts, such as this article, characters...

In complex analysis, the Riemann mapping theorem states that if U {\displaystyle U} is a non-empty simply connected open subset of the complex number...

and the theorem stating that every continuous function on a closed and bounded interval is uniformly continuous. Peter Gustav Lejeune Dirichlet was the...

Gustav Lejeune Dirichlet (1805–1859) is the eponym of many things. Theorems named Dirichlet's theorem: Dirichlet's approximation theorem (diophantine approximation)...

function field Dirichlet's unit theorem, S-unit Kummer extension Minkowski's theorem, Geometry of numbers Chebotarev's density theorem Ray class group...