A note on the gaps between consecutive zeros of the Riemann zeta-function

Assuming the Riemann Hypothesis, we show that infinitely often consecutive non-trivial zeros of the Riemann zeta-function differ by at most 0.5155 times the average spacing and infinitely often they differ by at least 2.69 times the average spacing.Comment: 7 pages. Submitted for publicatio

Simple zeros of modular L-functions

Assuming the generalized Riemann hypothesis, we prove quantitative estimates for the number of simple zeros on the critical line for the L-functions attached to classical holomorphic newforms.Comment: 46 page

Invariants of Legendrian Knots and Coherent Orientations

We provide a translation between Chekanov's combinatorial theory for invariants of Legendrian knots in the standard contact R^3 and a relative version of Eliashberg and Hofer's Contact Homology. We use this translation to transport the idea of ``coherent orientations'' from the Contact Homology world to Chekanov's combinatorial setting. As a result, we obtain a lifting of Chekanov's differential graded algebra invariant to an algebra over Z[t,t^{-1}] with a full Z grading.Comment: 32 pages, 17 figures; small technical corrections to proof of Thm 3.7 and example 4.

Non-stationary de Sitter cosmological models

In this note it is proposed a class of non-stationary de Sitter, rotating and non-rotating, solutions of Einstein's field equations with a cosmological term of variable function.Comment: 11 pages, Latex. International Journal of Modern Physics D (accepted for publication

[CI], [CII] and CO emission lines as a probe for alpha variations at low and high redshifts

The offsets between the radial velocities of the rotational transitions of carbon monoxide and the fine structure transitions of neutral and singly ionized carbon are used to test the hypothetical variation of the fine structure constant, alpha. From the analysis of the [CI] and [CII] fine structure lines and low J rotational lines of 12CO and 13CO, emitted by the dark cloud L1599B in the Milky Way disk, we find no evidence for fractional changes in alpha at the level of |$\Delta \alpha/\alpha$| < 3*10^-7. For the neighbour galaxy M33 a stringent limit on Delta alpha/alpha is set from observations of three HII zones in [CII] and CO emission lines: |$\Delta \alpha/\alpha$| < 4*10^-7. Five systems over the redshift interval z = 5.7-6.4, showing CO J=6-5, J=7-6 and [CII] emission, yield a limit on |$\Delta \alpha/\alpha$| < 1.3*10^-5. Thus, a combination of the [CI], [CII], and CO emission lines turns out to be a powerful tool for probing the stability of the fundamental physical constants over a wide range of redshifts not accessible to optical spectral measurements.Comment: 10 pages, 3 figures, 5 tables. Accepted for publication in MNRA