मेरोमॉर्फिक इसके अंग्रेजी अर्थ का उदाहरण

One considers a divisor as a set of constraints on meromorphic functions in the function field of C, defining L(D) as the vector space of functions having poles only at points of D with positive coefficient, at most as bad as the coefficient indicates, and having zeros at points of D with negative coefficient, with at least that multiplicity.

Let "fnof; and g be functions on either the entire complex plane or the unit disk, where g is meromorphic and "fnof; is analytic, such that wherever g has a pole of order m, f has a zero of order 2m (or equivalently, such that the product "fnof;g2 is holomorphic), and let c1, c2, c3 be constants.

showed that if A is the Laplacian of a compact Riemannian manifold then the Minakshisundaram–Pleijel zeta function converges and has an analytic continuation as a meromorphic function to all complex numbers, and extended this to elliptic pseudo-differential operators A on compact Riemannian manifolds.

converges absolutely for and extends to a meromorphic function defined for all complex with only one simple pole at , with residue.

These are never algebraic, though they have non-constant meromorphic functions.

Gun politics in the United States In mathematics, a Moishezon manifold is a compact complex manifold such that the field of meromorphic functions on each component has transcendence degree equal the complex dimension of the component:.

where L(kP) is the space of meromorphic functions on C whose order at P is at least -k and with no other poles.

He also described which points on Wg "minus; 1 are non-singular: they correspond to the effective divisors D of degree g "minus; 1 with no associated meromorphic functions other than constants.

In particular he computed their multiplicities also in terms of the number of independent meromorphic functions associated to D (Riemann-Kempf singularity theorem).

Hecke proved these L-functions have a meromorphic continuation to the whole complex plane, being analytic except for a simple pole of order 1 at s 1 when the character is trivial.

Using [analysis], more precisely the Poisson summation formula, he proved the functional equation and meromorphic continuation of the zeta integral and the Hecke L-function.

Iwasawa in his letter to Dieudonné derived on several pages not only the meromorphic continuation and functional equation of the L-function, he also proved finiteness of the class number and Dirichlet's theorem on units as immediate byproducts of the main computation.