Sup-norms of eigenfunctions in the level aspect for compact arithmetic surfaces, II: newforms and subconvexity

We improve upon the local bound in the depth aspect for sup-norms of newforms on $D^\times$, where $D$ is an indefinite quaternion division algebra over ${\mathbb {Q}}$. Our sup-norm bound implies a depth-aspect subconvexity bound for $L(1/2, f \times \theta _\chi )$, where $f$ is a (varying) newform on $D^\times$ of level $p^n$, and $\theta _\chi$ is an (essentially fixed) automorphic form on $\textrm {GL}_2$ obtained as the theta lift of a Hecke character $\chi$ on a quadratic field. For the proof, we augment the amplification method with a novel filtration argument and a recent counting result proved by the second-named author to reduce to showing strong quantitative decay of matrix coefficients of local newvectors along compact subsets, which we establish via $p$-adic stationary phase analysis. Furthermore, we prove a general upper bound in the level aspect for sup-norms of automorphic forms belonging to any family whose associated matrix coefficients have such a decay property.

A new subconvex bound for GL(3) L-functions in the t-aspect

We revisit Munshi’s proof of the [Formula: see text]-aspect subconvex bound for [Formula: see text] [Formula: see text]-functions, and we are able to remove the “conductor lowering” trick. This simplification along with a more careful stationary phase analysis allows us to improve Munshi’s bound to [Formula: see text]

Sub-Weyl subconvexity for Dirichlet -functions to prime power moduli

We prove a subconvexity bound for the central value $L(\frac{1}{2},{\it\chi})$ of a Dirichlet $L$-function of a character ${\it\chi}$ to a prime power modulus $q=p^{n}$ of the form $L(\frac{1}{2},{\it\chi})\ll p^{r}q^{{\it\theta}+{\it\epsilon}}$ with a fixed $r$ and ${\it\theta}\approx 0.1645<\frac{1}{6}$, breaking the long-standing Weyl exponent barrier. In fact, we develop a general new theory of estimation of short exponential sums involving $p$-adically analytic phases, which can be naturally seen as a $p$-adic analogue of the method of exponent pairs. This new method is presented in a ready-to-use form and applies to a wide class of well-behaved phases including many that arise from a stationary phase analysis of hyper-Kloosterman and other complete exponential sums.

Ribosome Hibernation Facilitates Tolerance of Stationary-Phase Bacteria to Aminoglycosides

ABSTRACTUpon entry into stationary phase, bacteria dimerize 70S ribosomes into translationally inactive 100S particles by a process called ribosome hibernation. Previously, we reported that the hibernation-promoting factor (HPF) ofListeria monocytogenesis required for 100S particle formation and facilitates adaptation to a number of stresses. Here, we demonstrate that HPF is required for the high tolerance of stationary-phase cultures to aminoglycosides but not to beta-lactam or quinolone antibiotics. The sensitivity of a Δhpfmutant to gentamicin was suppressed by the bacteriostatic antibiotics chloramphenicol and rifampin, which inhibit translation and transcription, respectively. Disruption of the proton motive force by the ionophore carbonyl cyanidem-chlorophenylhydrazone or mutation of genes involved in respiration also suppressed the sensitivity of the Δhpfmutant. Accordingly, Δhpfmutants had aberrantly high levels of ATP and reducing equivalents during prolonged stationary phase. Analysis of bacterial uptake of fluorescently labeled gentamicin demonstrated that the Δhpfmutant harbored increased intracellular levels of the drug. Finally, deletion of the main ribosome hibernation factor ofEscherichia coli, ribosome modulation factor (rmf), rendered these bacteria susceptible to gentamicin. Taken together, these data suggest that HPF-mediated ribosome hibernation results in repression of the metabolic activity that underlies aminoglycoside tolerance. HPF is conserved in nearly every bacterial pathogen, and the role of ribosome hibernation in antibiotic tolerance may have clinical implications.