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

Legendrian contact homology in R3\mathbb{R}^3

This is an introduction to Legendrian contact homology and the Chekanov-Eliashberg differential graded algebra, with a focus on the setting of Legendrian knots in $\mathbb{R}^3$.Comment: v3: 59 pages, 27 figures; introduction rewritten, sections 5 and 6 switched, many small revision

Critique of proposed limit to space--time measurement, based on Wigner's clocks and mirrors

Based on a relation between inertial time intervals and the Riemannian curvature, we show that space--time uncertainty derived by Ng and van Dam implies absurd uncertainties of the Riemannian curvature.Comment: 5 pages, LaTex, field "Author:" correcte

Legendrian and transverse twist knots

In 1997, Chekanov gave the first example of a Legendrian nonsimple knot type: the $m(5_2)$ knot. Epstein, Fuchs, and Meyer extended his result by showing that there are at least $n$ different Legendrian representatives with maximal Thurston--Bennequin number of the twist knot $K_{-2n}$ with crossing number $2n+1$. In this paper we give a complete classification of Legendrian and transverse representatives of twist knots. In particular, we show that $K_{-2n}$ has exactly $\lceil\frac{n^2}2\rceil$ Legendrian representatives with maximal Thurston--Bennequin number, and $\lceil\frac{n}{2}\rceil$ transverse representatives with maximal self-linking number. Our techniques include convex surface theory, Legendrian ruling invariants, and Heegaard Floer homology.Comment: 27 pages, v3: added figure, other minor changes, to appear in JEM

Climatic control on the peak discharge of glacier outburst floods

Lakes impounded by natural ice dams occur in many glacier regions. Their sudden emptying along subglacial paths can unleash similar to 1 km(3) of floodwater, but predicting the peak discharge of these subglacial outburst floods ('jokulhlaups') is notoriously difficult. To study how environmental factors control jokulhlaup magnitude, we use thermo- mechanical modelling to interpret a 40- year flood record from Merzbacher Lake in the Tian Shan. We show that the mean air temperature during each flood modulates its peak discharge, by influencing both the rate of meltwater input to the lake as it drains, and the lake- water temperature. The flood devastation potential thus depends sensitively on weather, and this dependence explains how regional climatic warming drives the rising trend of peak discharges in our dataset. For other subaerial ice- dammed lakes worldwide, regional warming will also promote higher- impact jokulhlaups by raising the likelihood of warm weather during their occurrence, unless other factors reduce lake volumes at flood initiation to outweigh this effect

Subconvexity for modular form L-functions in the t aspect

Modifying a method of Jutila, we prove a t aspect subconvexity estimate for L-functions associated to primitive holomorphic cusp forms of arbitrary level that is of comparable strength to Good's bound for the full modular group, thus resolving a problem that has been open for 35 years. A key innovation in our proof is a general form of Voronoi summation that applies to all fractions, even when the level is not squarefree.Comment: minor revisions; to appear in Adv. Math.; 30 page

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