A method for calculating spectral statistics based on random-matrix universality with an application to the three-point correlations of the Riemann zeros

We illustrate a general method for calculating spectral statistics that combines the universal (Random Matrix Theory limit) and the non-universal (trace-formula-related) contributions by giving a heuristic derivation of the three-point correlation function for the zeros of the Riemann zeta function. The main idea is to construct a generalized Hermitian random matrix ensemble whose mean eigenvalue density coincides with a large but finite portion of the actual density of the spectrum or the Riemann zeros. Averaging the random matrix result over remaining oscillatory terms related, in the case of the zeta function, to small primes leads to a formula for the three-point correlation function that is in agreement with results from other heuristic methods. This provides support for these different methods. The advantage of the approach we set out here is that it incorporates the determinental structure of the Random Matrix limit.Comment: 22 page

Two-point correlation function for Dirichlet L-functions

The two-point correlation function for the zeros of Dirichlet L-functions at a height E on the critical line is calculated heuristically using a generalization of the Hardy-Littlewood conjecture for pairs of primes in arithmetic progression. The result matches the conjectured Random-Matrix form in the limit as $E\rightarrow\infty$ and, importantly, includes finite-E corrections. These finite-E corrections differ from those in the case of the Riemann zeta-function, obtained in (1996 Phys. Rev. Lett. 77 1472), by certain finite products of primes which divide the modulus of the primitive character used to construct the L-function in question.Comment: 10 page

Arithmetic correlations over large finite fields

The auto-correlations of arithmetic functions, such as the von Mangoldt function, the M\"obius function and the divisor function, are the subject of classical problems in analytic number theory. The function field analogues of these problems have recently been resolved in the limit of large finite field size $q$. However, in this limit the correlations disappear: the arithmetic functions become uncorrelated. We compute averages of terms of lower order in $q$ which detect correlations. Our results show that there is considerable cancellation in the averaging and have implications for the rate at which correlations disappear when $q \rightarrow\infty$; in particular one cannot expect remainder terms that are of the order of the square-root of the main term in this context.Comment: The paper has been accepted by IMR

Letter, to Bill Kauffman and Warren Corman, from W.E. Keating, October 25, 1977

Letter discussing the 1977 Session of the Legislature and Senate Bill No. 130, Chapter 284 discussing historical preservation and Rarick Hall.https://scholars.fhsu.edu/rarick/1039/thumbnail.jp

A Case Study on Factors Influencing Retention of Mental Health Clinicians in a New Hampshire Community Mental Health Center

This study examined the perspectives of master-level clinical mental health providers and members of leadership at a Community Mental Health Center (CMHC) in New Hampshire, to understand clinician and leadership perspectives as to why master-level providers choose to continue working at CMHCs. Most prior research on turnover in such organizations has focused on why so many leave their positions, however this study instead focuses on factors related to the decision to stay at a specific CMHC in an urban area of New Hampshire. A single case study method was utilized to focus on masters-level mental health care providers with additional interviews with leadership at the CMHC. Some of the findings that will be explored is what draws providers to community mental health centers, the importance of connections with colleagues and leadership, and aspects of why master-level providers stay. The study contributes to the understanding of clinician retention in community mental health centers and provides recommendations for master-level providers, CMHC leadership, and clinical mental health educators. Some of the overarching themes that surface from the data were around why clinicians remain in the CMHC, the reasons why providers do the work they do each day, the draw to CMHC, and reasons why people master-level providers consider leaving a CMHC. Connections with leadership and supervisor were very important in why clinicians want to stay at the CMHC. Licensure contracts were also an area that was explored in this research. Clinicians and members of leadership provided their perspective on licensure contracts and the implementation of the contracts. This dissertation is available in open access at AURA (https://aura.antioch.edu/) and OhioLINK ETD Center (https://etd.ohiolink.edu)

Analysis of College Practices In Students Organization Accounting With Recommendations For A Standardized Procedure

The situation in regard to student organization accounting is very nearly chaotic . Colleges and universities have long realized that student organizations do not keep adequate records , but few of the smaller colleges have taken the necessary steps to remedy the situation. The problem was stated several years ago by T. G. Carlson, Business Hanager of the University of Arkansas, in a report to a group of business officers . In commenting upon the audit practices of schools, Mr. Carlson said, Many schools had a perfunctory supervision but only three or four had developed a thorough- going audit.” Mr. Harold C. Hand in his book Campus Activities declares that there has been a vast expansion of the student- activity program and this has given rise to numerous problems associated with the financing of these projects

Calibration of the spin-scan ozone imager aboard the dynamics Explorer 1 satellite

The calibration technique, which contains the calibrated backscattered radiance values necessary for performing the calibrations, is presented. The calibration constants for September to October 1981 to determine total columnar ozone from the Spin-Scan Ozone Imager (SOI), which is a part of the auroral imaging instrumentation aboard the Dynamics Explorer 1 Satellite, are provided. The precision of the SOI-derived total columnar ozone is estimated to be better than 2.4 percent. Linear regression analysis was used to calculate correlation coefficients between total columnar ozone obtained from Dobson ground stations and SOI which indicate that the SOI total columnar ozone determination is equally accurate for clear or cloudy weather conditions