Average values of modular L-series via the relative trace formula

First we reprove, using representation theory and the relative trace formula of Jacquet, an average value result of Duke for modular L-series at the critical center. We also establish a refinement. To be precise, the L-value which appears is L(1/2, f)L(1/2,f,\chi) (divided by the Petersson norm of f), and the average is over newforms f of prime level N and coefficients a_p(f), with \chi being an odd quadratic Dirichlet character of conductor -D and associated quadratic field K. For any prime p not dividing ND, the asymptotic as N goes to infinity is governed by a measure \mu_p, which is the Plancherel measure at p when \chi(p)=-1, but is new if \chi(p)=1; as p goes to infinity both measures approach the Sato-Tate measure. A particular consequence of our refinement is that for any non-empty interval J in [-2,2], there are infinitely many primes N, which are inert in K, such that for some f of level N, a_p(f) is in J and L(1/2, f)L(1/2,f,\chi) is non-zero

Tetramethylenedisulfotetramine

Tetramethylenedisulfotetramine (CAS 80-12-6), commonly referred to as TETS, was first synthesized in 1933 as a condensation product of sulfamide and formaldehyde. TETS was subsequently used as a rodenticide until banned worldwide in 1991. TETS is, however, still available illegally, primarily in rural China, and is responsible for accidental and intentional poisonings that cause a significant number of human deaths annually. TETS induces convulsive seizures mediated by antagonism of γ-amino-butyric acid (GABA)-mediated chloride channels. There are no known antidotes for TETS poisoning, and in cases of severe TETS intoxication that progress to status epilepticus, prognosis is poor even with aggressive anti-convulsant treatment

Perampanel inhibition of AMPA receptor currents in cultured hippocampal neurons.

Perampanel is an aryl substituted 2-pyridone AMPA receptor antagonist that was recently approved as a treatment for epilepsy. The drug potently inhibits AMPA receptor responses but the mode of block has not been characterized. Here the action of perampanel on AMPA receptors was investigated by whole-cell voltage-clamp recording in cultured rat hippocampal neurons. Perampanel caused a slow (τ∼1 s at 3 µM), concentration-dependent inhibition of AMPA receptor currents evoked by AMPA and kainate. The rates of block and unblock of AMPA receptor currents were 1.5×105 M-1 s-1 and 0.58 s-1, respectively. Perampanel did not affect NMDA receptor currents. The extent of block of non-desensitizing kainate-evoked currents (IC50, 0.56 µM) was similar at all kainate concentrations (3-100 µM), demonstrating a noncompetitive blocking action. Parampanel did not alter the trajectory of AMPA evoked currents indicating that it does not influence AMPA receptor desensitization. Perampanel is a selective negative allosteric AMPA receptor antagonist of high-affinity and slow blocking kinetics

Addendum to `Fake Projective Planes'

The addendum updates the results presented in the paper `Fake Projective Plane, Invent Math 168, 321-370 (2007)' and makes some additions and corrections. The fake projective planes are classified into twenty six classes. Together with a recent work of Donald Cartwright and Tim Steger, there is now a complete list of fake projective planes. There are precisely one hundred fake projective planes as complex surfaces classified up to biholomorphism.Comment: A more refined classification is given in the new versio

Non-coherence of arithmetic hyperbolic lattices

We prove, under the assumption of the virtual fibration conjecture for arithmetic hyperbolic 3-manifolds, that all arithmetic lattices in O(n,1), n> 4, and different from 7, are non-coherent. We also establish noncoherence of uniform arithmetic lattices of the simplest type in SU(n,1), n> 1, and of uniform lattices in SU(2,1) which have infinite abelianization.Comment: 26 pages, 3 figure

Tetramethylenedisulfotetramine alters Ca²⁺ dynamics in cultured hippocampal neurons: mitigation by NMDA receptor blockade and GABA(A) receptor-positive modulation.

Tetramethylenedisulfotetramine (TETS) is a potent convulsant that is considered a chemical threat agent. We characterized TETS as an activator of spontaneous Ca²⁺ oscillations and electrical burst discharges in mouse hippocampal neuronal cultures at 13-17 days in vitro using FLIPR Fluo-4 fluorescence measurements and extracellular microelectrode array recording. Acute exposure to TETS (≥ 2 µM) reversibly altered the pattern of spontaneous neuronal discharges, producing clustered burst firing and an overall increase in discharge frequency. TETS also dramatically affected Ca²⁺ dynamics causing an immediate but transient elevation of neuronal intracellular Ca²⁺ followed by decreased frequency of Ca²⁺ oscillations but greater peak amplitude. The effect on Ca²⁺ dynamics was similar to that elicited by picrotoxin and bicuculline, supporting the view that TETS acts by inhibiting type A gamma-aminobutyric acid (GABA(A)) receptor function. The effect of TETS on Ca²⁺ dynamics requires activation of N-methyl-D-aspartic acid (NMDA) receptors, because the changes induced by TETS were prevented by MK-801 block of NMDA receptors, but not nifedipine block of L-type Ca²⁺ channels. Pretreatment with the GABA(A) receptor-positive modulators diazepam and allopregnanolone partially mitigated TETS-induced changes in Ca²⁺ dynamics. Moreover, low, minimally effective concentrations of diazepam (0.1 µM) and allopregnanolone (0.1 µM), when administered together, were highly effective in suppressing TETS-induced alterations in Ca²⁺ dynamics, suggesting that the combination of positive modulators of synaptic and extrasynaptic GABA(A) receptors may have therapeutic potential. These rapid throughput in vitro assays may assist in the identification of single agents or combinations that have utility in the treatment of TETS intoxication

The virtual Haken conjecture: Experiments and examples

A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture says that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. Here, we discuss two interrelated topics concerning this conjecture. First, we describe computer experiments which give strong evidence that the Virtual Haken Conjecture is true for hyperbolic 3-manifolds. We took the complete Hodgson-Weeks census of 10,986 small-volume closed hyperbolic 3-manifolds, and for each of them found finite covers which are Haken. There are interesting and unexplained patterns in the data which may lead to a better understanding of this problem. Second, we discuss a method for transferring the virtual Haken property under Dehn filling. In particular, we show that if a 3-manifold with torus boundary has a Seifert fibered Dehn filling with hyperbolic base orbifold, then most of the Dehn filled manifolds are virtually Haken. We use this to show that every non-trivial Dehn surgery on the figure-8 knot is virtually Haken.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper12.abs.htm

p-adic Hodge-theoretic properties of \'etale cohomology with mod p coefficients, and the cohomology of Shimura varieties

We show that the mod p cohomology of a smooth projective variety with semistable reduction over K, a finite extension of Qp, embeds into the reduction modulo p of a semistable Galois representation with Hodge-Tate weights in the expected range (at least after semisimplifying, in the case of the cohomological degree > 1). We prove refinements with descent data, and we apply these results to the cohomology of unitary Shimura varieties, deducing vanishing results and applications to the weight part of Serre's conjecture.Comment: Essentially final version; to appear in Algebra and Number Theor

Distribution of catecholamine fibers in the cochlear nucleus of horseshoe bats and mustache bats

The glyoxylic-acid-induced fluorescence technique was applied to demonstrate patterns of catecholaminergic innervation within the auditory brainstem of echolocating bats and the house mouse. In the cochlear nucleus of the rufous horseshoe bat (Rhinolophus rouxi) and the mustache bat (Pteronotus parnelli), species-specific catecholaminergic innervation patterns are found that contrast with the relatively homogeneous innervation in the rodent. In both bats the subnuclei of the cochlear nucleus receive a differentially dense supply of catecholaminergic fibers, and within the subnuclei, the catecholamine innervation densities can be correlated with the tonotopic frequency representation. The areas devoted to the high-frequency echolocation calls are less densely innervated than those regions which are responsive to lower frequencies. Apart from this common scheme, there are noteworthy distinctions between the two bats which correlate with specialized cytoarchitectural features of the cochlear nucleus. The marginal cell group, located medially to the anteroventral cochlear nucleus of Pteronotus, receives the densest supply of catecholaminergic fibers of all auditory nuclei. This plexus is formed by a morphologically distinct population of catecholaminergic fibers

Cherednik algebras and Zhelobenko operators

We study canonical intertwining operators between induced modules of the trigonometric Cherednik algebra. We demonstrate that these operators correspond to the Zhelobenko operators for the affine Lie algebra of type A. To establish the correspondence, we use the functor of Arakawa, Suzuki and Tsuchiya which maps certain modules of the affine Lie algebra to modules of the Cherednik algebra