The Bergman tau functions are applied to the study of Picard group moduli spaces quadratic differentials with at most $n$ simple poles on genus $g$ complex algebraic curves. This generalizes our previous results holomorphic differentials.

of a Laurent series. If Op is the local ring of holomorphic functions around p. Take Mp the field of meromorphic functions around p, a principle part is just an element of the quotient groupMp/Op. The Mittag-Leffler question is, given a discrete set {pn} of points in S and a principle part at pn for each n, does there exist a meromorphic function f on S, holomorphic outside {pn}, whose principl...

Among the invariant factors g of a positive semidefinite analytic function f on R, those g whose zero set Y is a curve are called special. We show that if each special g is a sum of squares of global meromorphic functions on a neighbourhood of Y , then f is a sum of squares of global meromorphic functions. Here sums can be (convergent) infinite, but we also find some sufficient conditions to ge...

We study the normality of families of meromorphic functions related to a result of Drasin. We consider whether a family meromorphic functions F whose each function does not take zero is normal in D, if for every pair of functions f and g in F, f z and g z share ∞ or H f − 1 and H g − 1 share 0, whereH f : f k z ak−1f k−1 z · · · , a0f z . Some examples show that the conditions in our results ar...

We present the basics of two-body quantum-mechanical scattering theory and the theory of quantum resonances. The wave operators and S-matrix are constructed for smooth, compactly-supported potential perturbations of the Laplacian. The meromorphic continuation of the cut-off resolvent is proved for the same family of Schrödinger operators. Quantum resonances are defined as the poles of the merom...

*Correspondence: [email protected] 4School of Economic and Management, Guangzhou University of Chinese Medicine, Guangzhou, 510006, People’s Republic of China Full list of author information is available at the end of the article Abstract In the note, we study the normality of families of meromorphic functions. We consider whether a family of meromorphic functions F is normal in D if, for a no...

The Geng hierarchy is derived with the aid of Lenard recursion sequences. Based on Lax matrix, a hyperelliptic curve arithmetic genus n+1 introduced, from which meromorphic function ϕ ...