We show that for at least $$\frac{5}{13}$$ of the primitive Dirichlet characters $$\chi $$ large prime modulus, central value $$L(\frac{1}{2},\chi )$$ does not vanish, improving on previous best known result $$\frac{3}{8}$$ .

There are few general physical principles that protect the low-energy excitations of a quantum phase. Of these, Goldstone's theorem and Landau-Fermi liquid theory are the most relevant to solids. We investigate the stability of the resulting gapless excitations--Nambu-Goldstone bosons (NGBs) and Landau quasiparticles--when coupled to one another, which is of direct relevance to metals with a br...

J.L. Andersen proved that there is 5-torsion in the bottom nonvanishing homology group of the simplicial complex of graphs of degree at most two on seven vertices. We use this result to demonstrate that there is 5-torsion also in the bottom nonvanishing homology group of the matching complex M14 on 14 vertices. Combining our observation with results due to Bouc and to Shareshian and Wachs, we c...

A model is proposed to describe a transition from a charged black hole of mass M and charge Q to one of mass M and charge Q. The basic equations are derived from the non-vacuum Einstein field equations sourced by the Coulomb field and by a null scalar field with a nonvanishing trace anomaly. It is shown that the nonvanishing trace of the energy-momentum tensor prevents the formation of a naked ...

introduction: pulmonary tuberculosis is major problem worldwide and it is estimated one third the world population are already infected and each year 9 million people develop full blown tuberculosis of these 3 million die of the disease, annually. delay in diagnosis and treatment are major problems that play a significant role in all aspect of the disease from patient treatment to transmission ...

We extend the techniques developed by Millson and Raghunathan in [MR] to prove nonvanishing results for the cohomology of compact arithmetic quotients M of hyperbolic n-space H with values in the local coefficient systems associated to finite dimensional irreducible representations of the group SO(n, 1). We prove that all possible nonvanishing results compatible with the vanishing theorems of [...

In this note, we apply the method of Rodriguez Villegas and Yang (1996) to construct a family of infinite many theta series over the HilbertBlumenthal modular surfaces with a common zero. We also relate the nonvanishing of the central L-values of certain Hecke characters of non-biquadratic CM number fields of degree 4 to the nonvanishing of theta functions at CM points in the Hilbert-Blumenthal...