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The Chebotarev density theorem is a complicated theorem in algebraic number theory which yields an asymptotic formula for the density of prime ideals of a number field K that ...

A theorem which states that the analytic and topological "indices" are equal for any elliptic differential operator on an n-dimensional compact smooth C^infty boundaryless ...

Let a_n>=0 and suppose sum_(n=1)^inftya_ne^(-an)∼1/a as a->0^+. Then sum_(n<=x)a_n∼x as x->infty. This theorem is a step in the proof of the prime number theorem, but has ...

If two projective pencils of curves of orders n and n^' have no common curve, the locus of the intersections of corresponding curves of the two is a curve of order n+n^' ...

Church proved several important theorems that now go by the name Church's theorem. One of Church's theorems states that there is no consistent decidable extension of Peano ...

Jung's theorem states that the generalized diameter D of a compact set X in R^n satisfies D>=Rsqrt((2(n+1))/n), where R is the circumradius of X (Danzer et al. 1963). This ...

If f(z) is continuous in a region D and satisfies ∮_gammafdz=0 for all closed contours gamma in D, then f(z) is analytic in D. Morera's theorem does not require simple ...

Consider a reference triangle DeltaABC with circumcenter O and orthocenter H, and let DeltaA^*B^*C^* be its reflection triangle. Then Musselman's theorem states that the ...

An analytic function f(z) whose Laurent series is given by f(z)=sum_(n=-infty)^inftya_n(z-z_0)^n, (1) can be integrated term by term using a closed contour gamma encircling ...

For omega a differential (k-1)-form with compact support on an oriented k-dimensional manifold with boundary M, int_Mdomega=int_(partialM)omega, (1) where domega is the ...