Towards the Deep Riemann Hypothesis for GLn\mathrm{GL}_{n}

We explicate the deep Riemann hypothesis for the general linear group $\mathrm{GL}_{n}$ on the convergence of normalised Euler products of standard $L$-functions on the critical line. It conditionally improves upon the error term in the prime number theorem beyond what the grand Riemann hypothesis predicts. Furthermore, we discuss the Chebyshev bias for Satake parameters on $\mathrm{GL}_{n}$ from the perspective of the deep Riemann hypothesis.Comment: 17 page

The shock process and light element production in supernovae envelopes

Detailed hydrodynamic modeling of the passage of supernova shocks through the hydrogen envelopes of blue and red progenitor stars was carried out to explore the sensitivity to model conditions of light element production (specifically Li-7 and B-11) which was noted by Dearborn, Schramm, Steigman and Truran (1989) (DSST). It is found that, for stellar models with M is less than or approximately 100 M solar mass, current state of the art supernova shocks do not produce significant light element yields by hydrodynamic processes alone. The dependence of this conclusion on stellar models and on shock strengths is explored. Preliminary implications for Galactic evolution of lithium are discussed, and it is suspected that intermediate mass red giant stars may be the most consistent production site for lithium

C. elegans PlexinA PLX-1 mediates a cell contact-dependent stop signal in vulval precursor cells

AbstractPLX-1 is a PlexinA transmembrane protein in Caenorhabditis elegans, and the transmembrane-type semaphorin, SMP-1, is a ligand for PLX-1. The SMP-1/PLX-1 system has been shown to be necessary for proper epidermal morphogenesis in the male tail and seam cells. Here, we show that the SMP-1/PLX-1 system also regulates vulval morphogenesis. In plx-1 and smp-1 mutants, hermaphrodites sometimes exhibit a protruding vulva or multiple vulva-like protrusions. Throughout the vulval development of plx-1 and smp-1 mutants, the arrangement of vulval cells is often disrupted. In the initial step of vulval morphogenesis, vulval precursor cells (VPCs) are generated normally but are subsequently arranged abnormally in mutants. Continuous observation revealed that plx-1 VPC fails to terminate longitudinal extension after making contact with neighbor VPCs. The arrangement defects of VPCs in plx-1 and smp-1 mutants are rescued by expressing the respective cDNA in VPCs. plx-1::egfp and smp-1::egfp transgenes are both expressed in all vulval cells, including VPCs, throughout vulval development. We propose that the SMP-1/PLX-1 system is responsible for a cell contact-mediated stop signal for VPC extension. Analyses using cell fate-specific markers showed that the arrangement defects of VPCs also affect cell fate specification and cell lineages, but in a relatively small fraction of plx-1 mutants