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

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.

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

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