In mathematics and in particular the field of complex analysis, Hurwitz's theorem is a theorem associating the zeroes of a sequence of holomorphic, compact...

Hurwitz's theorem can refer to several theorems named after Adolf Hurwitz: Hurwitz's theorem (complex analysis) Riemann–Hurwitz formula in algebraic geometry...

Riemann–Roch theorem. Argument principle Control theory § Stability Filter design Filter (signal processing) Gauss–Lucas theorem Hurwitz's theorem (complex analysis)...

mathematics, the Routh–Hurwitz theorem gives a test to determine whether all roots of a given polynomial lie in the left-half complex plane. Polynomials with...

C}(0)=N_{g}(K).} Fundamental theorem of algebra – Every polynomial has a real or complex root Hurwitz's theorem (complex analysis) – Limit of roots of sequence...

The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension...

Hurwitz scheme Hurwitz surface Hurwitz zeta function Hurwitz's automorphisms theorem Hurwitz's theorem (complex analysis) Hurwitz's theorem (composition...

analysis) Hurwitz's automorphisms theorem (algebraic curves) Hurwitz's theorem (complex analysis) Identity theorem (complex analysis) Identity theorem for Riemann...

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...

reals, complex numbers, quaternions and octonions are all normed division algebras over R {\displaystyle \mathbb {R} } . By Hurwitz's theorem they are...

is quite safe). This formula is known as the Riemann–Hurwitz formula and also as Hurwitz's theorem. Another useful form of the formula is: χ ( S ′ ) −...

In mathematics, Hurwitz's theorem is a theorem of Adolf Hurwitz (1859–1919), published posthumously in 1923, solving the Hurwitz problem for finite-dimensional...

Sturm's theorem, this gives the number of roots of P such that Q(a) > 0 and the number of roots of P such that Q(a) < 0. Routh–Hurwitz theorem Hurwitz's theorem...

Marden's theorem Bôcher's theorem Sendov's conjecture Routh–Hurwitz theorem Hurwitz's theorem (complex analysis) Descartes' rule of signs Rouché's theorem Properties...

In mathematics, the Carathéodory kernel theorem is a result in complex analysis and geometric function theory established by the Greek mathematician Constantin...

duality Branching theorem Hurwitz's automorphisms theorem Identity theorem for Riemann surfaces Riemann–Roch theorem Riemann–Hurwitz formula Farkas & Kra...

principle of complex analysis requires no eigenvalue continuity of any kind. For a brief discussion and clarification, see. The Gershgorin circle theorem is useful...

of isometries of an hyperbolic surface of genus g {\displaystyle g} . Hurwitz's bound then implies that the maximal order is equal to 84 ( g − 1 ) {\displaystyle...

In matrix theory, the Perron–Frobenius theorem, proved by Oskar Perron (1907) and Georg Frobenius (1912), asserts that a real square matrix with positive...

derived by employing the functional equation together with Hurwitz's formula, given above. Hurwitz's zeta function occurs in a variety of disciplines. Most...

complex analysis include most notably the introduction of Riemann surfaces, breaking new ground in a natural, geometric treatment of complex analysis...

normed division algebras over the real numbers are also very rare: Hurwitz's theorem says that there are only four: R {\displaystyle \mathbb {R} } , C...

Sturm's theorem in evaluating Cauchy indices. Hurwitz derived his conditions differently. The criterion is related to Routh–Hurwitz theorem. From the...

Belevitch's theorem is a theorem in electrical network analysis due to the Russo-Belgian mathematician Vitold Belevitch (1921–1999). The theorem provides...

algebra with involution of twice the dimension.: 45  Hurwitz's theorem states that the reals, complex numbers, quaternions, and octonions are the only finite-dimensional...

quite safe). This formula is known as the Riemann–Hurwitz formula and also as Hurwitz's theorem. Hurwitz-Courant, Vorlesunger über allgemeine Funcktionen...

factorization theorem—that any entire function can be written as a product over its zeros in the complex plane; a generalization of the fundamental theorem of algebra...

circle group U(1) of unit modulus complex numbers. It is a theorem that every character of T is one of the complex exponentials e n ( x ) = e 2 π i n...

connected semisimple Lie groups and complex semisimple Lie algebras goes sometimes under the name of Weyl's theorem. A related result, that the universal...

In the mathematical field of complex analysis, Nevanlinna theory is part of the theory of meromorphic functions. It was devised in 1925, by Rolf Nevanlinna...