Conjectures on the logarithmic derivatives of Artin L-functions II

We formulate a general conjecture relating Chern classes of subbundles of Gauss-Manin bundles in Arakelov geometry to logarithmic derivatives of Artin L-functions of number fields. This conjecture may be viewed as a far-reaching generalisation of the (Lerch-)Chowla-Selberg formula computing logarithms of periods of elliptic curves in terms of special values of the $\Gamma$-function. We prove several special cases of this conjecture in the situation where the involved Artin characters are Dirichlet characters. This article contains the computations promised in the article {\it Conjectures sur les d\'eriv\'ees logarithmiques des fonctions L d'Artin aux entiers n\'egatifs}, where our conjecture was announced. We also give a quick introduction to the Grothendieck-Riemann-Roch theorem and to the geometric fixed point formula, which form the geometric backbone of our conjecture.Comment: 54 page

On the determinant bundles of abelian schemes

Let \pi:\CA\ra S be an abelian scheme over a scheme $S$ which is quasi-projective over an affine noetherian scheme and let \CL be a symmetric, rigidified, relatively ample line bundle on \CA. We show that there is an isomorphism \det(\pi_*\CL)^{\o times 24}\simeq\big(\pi_*\omega_{\CA}^{\vee}\big)^{\o times 12d} of line bundles on $S$, where $d$ is the rank of the (locally free) sheaf \pi_*\CL. We also show that the numbers 24 and $12d$ are sharp in the following sense: if $N>1$ is a common divisor of 12 and 24, then there are data as above such that \det(\pi_*\CL)^{\o times (24/N)}\not\simeq\big(\pi_*\omega_{\CA}^{\vee}\big)^{\o times (12d/N)}.Comment: 8 page

On a canonical class of Green currents for the unit sections of abelian schemes

We show that on any abelian scheme over a complex quasi-projective smooth variety, there is a Green current for the zero-section, which is axiomatically determined up to $\partial$ and $\bar\partial$-exact differential forms. This current generalizes the Siegel functions defined on elliptic curves. We prove generalizations of classical properties of Siegel functions, like distribution relations, limit formulae and reciprocity laws.Comment: 42 page

Formes automorphes et theoremes de Riemann-Roch arithmetiques

Nous construisons trois familles de formes automorphes au moyen du theoreme de Riemann-Roch arithmetique et de la formule de Lefschetz arithmetique. Deux de ces familles ont deja ete construites par Yoshikawa et notre construction met en lumiere leur origine arithmetique. ----- We construct three families of automorphic forms following the arithmetic Riemann-Roch theorem and the arithmetic Lefschetz formula. Two of these families were already constructed by Yoshikawa and our construction illuminates their arithmetic origin.Comment: 16 pages, in Frenc

Information Flow in Secret Sharing Protocols

The entangled graph states have emerged as an elegant and powerful quantum resource, indeed almost all multiparty protocols can be written in terms of graph states including measurement based quantum computation (MBQC), error correction and secret sharing amongst others. In addition they are at the forefront in terms of implementations. As such they represent an excellent opportunity to move towards integrated protocols involving many of these elements. In this paper we look at expressing and extending graph state secret sharing and MBQC in a common framework and graphical language related to flow. We do so with two main contributions. First we express in entirely graphical terms which set of players can access which information in graph state secret sharing protocols. These succinct graphical descriptions of access allow us to take known results from graph theory to make statements on the generalisation of the previous schemes to present new secret sharing protocols. Second, we give a set of necessary conditions as to when a graph with flow, i.e. capable of performing a class of unitary operations, can be extended to include vertices which can be ignored, pointless measurements, and hence considered as unauthorised players in terms of secret sharing, or error qubits in terms of fault tolerance. This offers a way to extend existing MBQC patterns to secret sharing protocols. Our characterisation of pointless measurements is believed also to be a useful tool for further integrated measurement based schemes, for example in constructing fault tolerant MBQC schemes

A comparison of mean winds and gravity wave activity in the northern and southern polar MLT

Mean winds and waves observed in the mesosphere and lower thermosphere with MF radars located at Davis (69°S, 78°E) and Poker Flat (65°N, 147°W) are compared. Measurements covering the period from 1999 to mid 2000 show differences in the strength of the horizontal wind fields. In the southern hemisphere the zonal and meridional winds reach their maximum values near the summer solstice, but are delayed by 2–3 weeks in the northern hemisphere. Gravity wave variances also show significant differences, as do the strength of vertical velocities.Andrew Dowdy and Robert A. Vincent, Kiyoshi Igarashi and Yasuhiro Murayama, Damian J. Murph

Explanation for Anomalous Shock Temperatures Measured by Neutron Resonance Spectroscopy

Neutron resonance spectrometry (NRS) has been used to measure the temperature inside Mo samples during shock loading. The temperatures obtained were significantly higher than predicted assuming ideal hydrodynamic loading. The effect of plastic flow and non-ideal projectile behavior were assessed. Plastic flow was calculated self-consistently with the shock jump conditions: this is necessary for a rigorous estimate of the locus of shock states accessible. Plastic flow was estimated to contribute a temperature rise of 53K compared with hydrodynamic flow. Simulations were performed of the operation of the explosively-driven projectile system used to induce the shock in the Mo sample. The simulations predicted that the projectile was significantly curved on impact, and still accelerating. The resulting spatial variations in load, including radial components of velocity, were predicted to increase the apparent temperature that would be deduced from the width of the neutron resonance by 160K. These corrections are sufficient to reconcile the apparent temperatures deduced using NRS with the accepted properties of Mo, in particular its equation of state.Comment: near-final version, waiting for final consent from an autho

The Molloy Student Literary Magazine Volume 12

The Molloy Student Literary Magazine, sponsored by Molloy College’s Office of Student Affairs, is devoted to publishing the best previously unpublished works of prose, poetry, drama, literary review, criticism, and other literary genres, that the Molloy student community has to offer. The journal welcomes submissions, for possible publication, from currently enrolled Molloy students at all levels. All submitted work will undergo a review process initiated by the Managing Editor prior to a decision being made regarding publication of said work. Given sufficient content, The Molloy Student Literary Magazine is published twice annually in Spring and Fall. Interested contributors from the currently enrolled Molloy student community should send work via e-mail attachment and brief cover letter (including a two-sentence biographical statement) to: Dr. Damian Ward Hey, Managing Editor, The Molloy Student Literary Magazine: [email protected]. Enrolled students who are interested in becoming members of The Molloy Student Literary Magazine staff may e-mail letters of inquiry. Excelsior!https://digitalcommons.molloy.edu/eng_litmag/1004/thumbnail.jp

The Molloy Student Literary Magazine Volume 14

The Molloy Student Literary Magazine, sponsored by Molloy College’s Office of Student Affairs, is devoted to publishing the best previously unpublished works of prose, poetry, drama, literary review, criticism, and other literary genres, that the Molloy student community has to offer. The journal welcomes submissions, for possible publication, from currently enrolled Molloy students at all levels. All submitted work will undergo a review process initiated by the Managing Editor prior to a decision being made regarding publication of said work. Given sufficient content, The Molloy Student Literary Magazine is published twice annually in Spring and Fall.https://digitalcommons.molloy.edu/eng_litmag/1006/thumbnail.jp