Finiteness of irreducible holomorphic eta quotients of a given level

We show that for any positive integer N, there are only finitely many holomorphic eta quotients of level N, none of which is a product of two holomorphic eta quotients other than 1 and itself. This result is an analog of Zagier’s conjecture/Mersmann’s theorem which states that of any given weight, there are only finitely many irreducible holomorphic eta quotients, none of which is an integral rescaling of another eta quotient. We construct such eta quotients for all cubefree levels. In particular, our construction demonstrates the existence of irreducible holomorphic eta quotients of arbitrarily large weights

Sovereign debt, creditor-country governments, and multilateral institutions

External Debt

An Atypical Case of Pelvic Leiomyomatosis Peritonealis Disseminata

An exceptional case of Leiomyomatosis peritonealis disseminata which occurred in a perimenopausal woman was mistaken for ovarian malignancy at laparotomy as it had extensive involvement of the pelvic peritoneum without a trace of leiomyoma in uterus and cervix

Stereochemical properties of the OH molecule in combined electric and magnetic fields: analytic results

The stereochemical properties of the ultracold ground state OH molecule in the presence of electric and magnetic fields are currently of considerable interest. For example, relevant quantities such as molecular alignment and orientation, calculated numerically by using large basis sets, have lately appeared in the literature. In this work, based on our recent exact solution to an effective eight-dimensional matrix Hamiltonian for the molecular ground state, we present analytic expressions for the stereochemical properties of OH. Our results require the solution of algebraic equations only, agree well with the aforementioned fully numerical calculations, provide compact expressions for simple field geometries, allow ready access to relatively unexplored parameter space, and yield straightforwardly higher moments of the molecular axis distribution.Comment: 8 pages, 9 figure