Curves of every genus with many points, I: Abelian and toric families

Let N_q(g) denote the maximal number of F_q-rational points on any curve of genus g over the finite field F_q. Ihara (for square q) and Serre (for general q) proved that limsup_{g-->infinity} N_q(g)/g > 0 for any fixed q. In their proofs they constructed curves with many points in infinitely many genera; however, their sequences of genera are somewhat sparse. In this paper, we prove that lim_{g-->infinity} N_q(g) = infinity. More precisely, we use abelian covers of P^1 to prove that liminf_{g-->infinity} N_q(g)/(g/log g) > 0, and we use curves on toric surfaces to prove that liminf_{g-->infty} N_q(g)/g^{1/3} > 0; we also show that these results are the best possible that can be proved with these families of curves.Comment: LaTeX, 20 page

Quasi-shuffle products revisited

Quasi-shuffle products, introduced by the first author, have been useful in studying multiple zeta values and some of their analogues and generalizations. The second author, together with Kajikawa, Ohno, and Okuda, significantly extended the definition of quasi-shuffle algebras so it could be applied to multiple zeta q-values. This article extends some of the algebraic machinery of the first author's original paper to the more general definition, and uses this extension to obtain various algebraic formulas in the quasi-shuffle algebra in a transparent way. Some applications to multiple zeta values, interpolated multiple zeta values, multiple q-zeta values, and multiple polylogarithms are given.Comment: This is an extensively revised and expanded version of the Max Planck Institute preprint (MPIM 2012-16) with the same title. 27 Oct 16: minor revision and corrections 3 Apr 17: additional revision and correction

Explosive fragmentation of thin ceramic tube using pulsed power

This study experimentally examined the explosive fragmentation of thin ceramic tubes using pulsed power. A thin ceramic tube was threaded on a thin copper wire, and high voltage was applied to the wire using a pulsed power generator. This melted the wire and the resulting vapor put pressure on the ceramic tube, causing it to fragment. We examined the statistical properties of the fragment mass distribution. The cumulative fragment mass distribution obeyed the double exponential or power-law with exponential decay. Both distributions agreed well with the experimental data. We also found that the weighted mean fragment mass was scaled by the multiplicity. This result was similar to impact fragmentation, except for the crossover point. Finally, we obtained universal scaling for fragmentation, which is applicable to both impact and explosive fragmentation.Comment: 5 pages, 6 figure

Microscopic observation of superconducting fluctuations in κ\kappa-(BEDT-TTF)2_{2}Cu[N(CN)2_{2}]Br by 13^{13}C NMR spectroscopy

We performed $^{13}$C-NMR experiment and measured spin-lattice relaxation rate divided by temperature $1/T_{1}T$ near the superconducting (SC) transition temperature $T_{c}$ in $\kappa$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Br ($\kappa$-Br salt), and $\kappa$-(BEDT-TTF)$_{2}$Cu(NCS)$_{2}$ ($\kappa$-NCS salt). We observed the reduction of $1/T_{1}T$ starting at the temperature higher than $T_c$ in $\kappa$-Br salt. Microscopic observation of quasi-particle density of states in the fluctuating SC state revealed the effects of short-range Cooper pairs induced in the normal state to the quasi-particle density of states. We also performed systematic measurements in the fields both parallel and perpendicular to the conduction plane in $\kappa$-Br and $\kappa$-NCS salts, and confirmed that the reduction of $1/T_{1}T$ above $T_{c}$ is observed only in $\kappa$-Br salt regardless of the external field orientation.Comment: Accepted for publication in PR