Random matrix models for Gram's law

Gram's Law refers to the empirical observation that the zeros of the Riemann zeta function typically alternate with certain prescribed points, called Gram points. Although this pattern does not hold true for each and every zero, numerical results suggest that, as the height up the critical line increases, the proportion of zeros that obey Gram's Law converges to a finite, non-zero limit. It is also well-known that the eigenvalues of random unitary matrices provide a good statistical model for the distribution of zeros of the zeta function, so one could try to determine the value of this limit by analyzing an analogous model for Gram's Law in the framework of Random Matrix Theory. In this thesis, we will review an existing model based on random unitary matrices, for which the limit can be computed analytically, but has the wrong rate of convergence. We will then present an alternative model that uses random special unitary matrices, which gives the correct convergence rate, and discuss the large-N limit of this model. We shall conclude that at very large heights up the critical line, the local distribution of the zeta zeros is the same with respect to any sequence of points that are spaced like the Gram points. For the purpose of this thesis, we will assume throughout that all Gram points are different from zeta zeros, although this is not a proven fact

Development of an automated test program for the ATLAS Local Trigger Processor Interface

The ATLAS detector at the Large Hadron Collider (LHC) at CERN uses a three-level trigger system. The Level-1 trigger is a synchronous system operating at the bunch crossing (BC) frequency of 40.08 MHz of the LHC. It uses information on clusters and global energy in the calorimeters and on tracks found in the dedicated muon trigger detectors. The Level-1 central trigger consists of the Muon-to-Central-Trigger-Processor Interface (MUCTPI), the Central Trigger Processor (CTP) and the Timing, Trigger and Control (TTC) partitions

Differential Higgs boson pair production at next-to-next-to-leading order in QCD

We report on the first fully differential calculation for double Higgs boson production through gluon fusion in hadron collisions up to next-to-next-to-leading order (NNLO) in QCD perturbation theory. The calculation is performed in the heavy-top limit of the Standard Model, and in the phenomenological results we focus on pp collisions at s√=14 s=14TeV. We present differential distributions through NNLO for various observables including the transverse-momentum and rapidity distributions of the two Higgs bosons. NNLO corrections are at the level of 10%-25% with respect to the next-to-leading order (NLO) prediction with a residual scale uncertainty of 5%-15% and an overall mild phase-space dependence. Only at NNLO the perturbative expansion starts to converge yielding overlapping scale uncertainty bands between NNLO and NLO in most of the phase-space. The calculation includes NLO predictions for pp → HH + jet + X. Corrections to the corresponding distributions exceed 50% with a residual scale dependence of 20%-30%