343 research outputs found
A central limit theorem for the zeroes of the zeta function
On the assumption of the Riemann hypothesis, we generalize a central limit
theorem of Fujii regarding the number of zeroes of Riemann's zeta function that
lie in a mesoscopic interval. The result mirrors results of Soshnikov and
others in random matrix theory. In an appendix we put forward some general
theorems regarding our knowledge of the zeta zeroes in the mesoscopic regime.Comment: 22 pages. Incorporates referees suggestions. Contains minor
corrections to published versio
Representations of integers by certain positive definite binary quadratic forms
We prove part of a conjecture of Borwein and Choi concerning an estimate on
the square of the number of solutions to n=x^2+Ny^2 for a squarefree integer N.Comment: 8 pages, submitte
Rational Design of Novel Anticancer Small-Molecule RNA m6A Demethylase ALKBH5 Inhibitors
The RNA 6-N-methyladenosine (m6A) demethylase ALKBH5 has been shown to be oncogenic in several cancer types, including leukemia and glioblastoma. We present here the target-tailored development and first evaluation of the antiproliferative effects of new ALKBH5 inhibitors. Two compounds, 2-[(1-hydroxy-2-oxo-2-phenylethyl)sulfanyl]acetic acid (3) and 4-{[(furan-2-yl)methyl]amino}-1,2-diazinane-3,6-dione (6), with IC50 values of 0.84 mu M and 1.79 mu M, respectively, were identified in high-throughput virtual screening of the library of 144 000 preselected compounds and subsequent verification of hits in an m6A antibody-based enzyme-linked immunosorbent assay (ELISA) enzyme inhibition assay. The effect of these compounds on the proliferation of selected target cancer cell lines was then measured. In the case of three leukemia cell lines (HL-60, CCRF-CEM, and K562) the cell proliferation was suppressed at low micromolar concentrations of inhibitors, with IC50 ranging from 1.38 to 16.5 mu M. However, the effect was low or negligible in the case of another leukemia cell line, Jurkat, and the glioblastoma cell line A-172. These results demonstrate the potential of ALKBH5 inhibition as a cancer-cell-type-selective antiproliferative strategy.Peer reviewe
Random matrix theory, the exceptional Lie groups, and L-functions
There has recently been interest in relating properties of matrices drawn at
random from the classical compact groups to statistical characteristics of
number-theoretical L-functions. One example is the relationship conjectured to
hold between the value distributions of the characteristic polynomials of such
matrices and value distributions within families of L-functions. These
connections are here extended to non-classical groups. We focus on an explicit
example: the exceptional Lie group G_2. The value distributions for
characteristic polynomials associated with the 7- and 14-dimensional
representations of G_2, defined with respect to the uniform invariant (Haar)
measure, are calculated using two of the Macdonald constant term identities. A
one parameter family of L-functions over a finite field is described whose
value distribution in the limit as the size of the finite field grows is
related to that of the characteristic polynomials associated with the
7-dimensional representation of G_2. The random matrix calculations extend to
all exceptional Lie groupsComment: 14 page
The Selberg trace formula for Dirac operators
We examine spectra of Dirac operators on compact hyperbolic surfaces.
Particular attention is devoted to symmetry considerations, leading to
non-trivial multiplicities of eigenvalues. The relation to spectra of
Maass-Laplace operators is also exploited. Our main result is a Selberg trace
formula for Dirac operators on hyperbolic surfaces
Advection of vector fields by chaotic flows
We have introduced a new transfer operator for chaotic flows whose leading
eigenvalue yields the dynamo rate of the fast kinematic dynamo and applied
cycle expansion of the Fredholm determinant of the new operator to evaluation
of its spectrum. The theory hs been tested on a normal form model of the vector
advecting dynamical flow. If the model is a simple map with constant time
between two iterations, the dynamo rate is the same as the escape rate of
scalar quantties. However, a spread in Poincar\'e section return times lifts
the degeneracy of the vector and scalar advection rates, and leads to dynamo
rates that dominate over the scalar advection rates. For sufficiently large
time spreads we have even found repellers for which the magnetic field grows
exponentially, even though the scalar densities are decaying exponentially.Comment: 12 pages, Latex. Ask for figures from [email protected]
Some recursive formulas for Selberg-type integrals
A set of recursive relations satisfied by Selberg-type integrals involving
monomial symmetric polynomials are derived, generalizing previously known
results. These formulas provide a well-defined algorithm for computing
Selberg-Schur integrals whenever the Kostka numbers relating Schur functions
and the corresponding monomial polynomials are explicitly known. We illustrate
the usefulness of our results discussing some interesting examples.Comment: 11 pages. To appear in Jour. Phys.
Asymptotic stability of small gap solitons in nonlinear Dirac equations
This is the published version, also available here: http://dx.doi.org/10.1063/1.4731477.We prove dispersive decay estimates for the one-dimensional Dirac operator and use them to prove asymptotic stability of small gap solitons in the nonlinear Dirac equations with quintic and higher-order nonlinear terms
Correlation functions in conformal Toda field theory I
Two-dimensional sl(n) quantum Toda field theory on a sphere is considered.
This theory provides an important example of conformal field theory with higher
spin symmetry. We derive the three-point correlation functions of the
exponential fields if one of the three fields has a special form. In this case
it is possible to write down and solve explicitly the differential equation for
the four-point correlation function if the fourth field is completely
degenerate. We give also expressions for the three-point correlation functions
in the cases, when they can be expressed in terms of known functions. The
semiclassical and minisuperspace approaches in the conformal Toda field theory
are studied and the results coming from these approaches are compared with the
proposed analytical expression for the three-point correlation function. We
show, that in the framework of semiclassical and minisuperspace approaches
general three-point correlation function can be reduced to the
finite-dimensional integral.Comment: 54 pages, JHEP styl
Equidistribution Rates, Closed String Amplitudes, and the Riemann Hypothesis
We study asymptotic relations connecting unipotent averages of
automorphic forms to their integrals over the moduli space
of principally polarized abelian varieties. We obtain reformulations of the
Riemann hypothesis as a class of problems concerning the computation of the
equidistribution convergence rate in those asymptotic relations. We discuss
applications of our results to closed string amplitudes. Remarkably, the
Riemann hypothesis can be rephrased in terms of ultraviolet relations occurring
in perturbative closed string theory.Comment: 15 page
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