Dirac-K\"ahler particle in Riemann spherical space: boson interpretation

In the context of the composite boson interpretation, we construct the exact general solution of the Dirac--K\"ahler equation for the case of the spherical Riemann space of constant positive curvature, for which due to the geometry itself one may expect to have a discrete energy spectrum. In the case of the minimal value of the total angular momentum, $j=0$, the radial equations are reduced to second-order ordinary differential equations, which are straightforwardly solved in terms of the hypergeometric functions. For non-zero values of the total angular momentum, however, the radial equations are reduced to a pair of complicated fourth-order differential equations. Employing the factorization approach, we derive the general solution of these equations involving four independent fundamental solutions written in terms of combinations of the hypergeometric functions. The corresponding discrete energy spectrum is then determined via termination of the involved hypergeometric series, resulting in quasi-polynomial wave-functions. The constructed solutions lead to notable observations when compared with those for the ordinary Dirac particle. The energy spectrum for the Dirac-K\"ahler particle in spherical space is much more complicated. Its structure substantially differs from that for the Dirac particle since it consists of two paralleled energy level series each of which is twofold degenerate. Besides, none of the two separate series coincides with the series for the Dirac particle. Thus, the Dirac--K\"ahler field cannot be interpreted as a system of four Dirac fermions. Additional arguments supporting this conclusion are discussed

Negative moments of the Riemann zeta-function

Assuming the Riemann Hypothesis we study negative moments of the Riemann zeta-function and obtain asymptotic formulas in certain ranges of the shift in $\zeta(s)$. For example, integrating $|\zeta(1/2+\alpha+it)|^{-2k}$ with respect to $t$ from $T$ to $2T$, we obtain an asymptotic formula when the shift $\alpha$ is roughly bigger than $\frac{1}{\log T}$ and $k < 1/2$. We also obtain non-trivial upper bounds for much smaller shifts, as long as $\log\frac{1}{\alpha} \ll \log \log T$. This provides partial progress towards a conjecture of Gonek on negative moments of the Riemann zeta-function, and settles the conjecture in certain ranges. As an application, we also obtain an upper bound for the average of the generalized M\"{o}bius function.Comment: 36 page

Type-I contributions to the one and two level densities of quadratic Dirichlet LL--functions over function fields

Using the Ratios Conjecture, we write down precise formulas with lower order terms for the one and the two level densities of zeros of quadratic Dirichlet $L$--functions over function fields. We denote the various terms arising as Type-$0$, Type-I and Type-II contributions. When the support of the Fourier transform of the test function is sufficiently restricted, we rigorously compute the Type-$0$ and Type-I terms and confirm that they match the conjectured answer. When the restrictions on the support are relaxed, our results suggest that Type-II contributions become important in the two level density.Comment: 23 page

Does allochthonous disscolved organic matter increase during summer algal bloom conditions in an agricultural reservoir?

Cyanobacterial harmful algal blooms (cyanoHABs) are increasing in frequency worldwide. CyanoHABs can produce toxins (e.g., microcystin), which can be a contaminant in recreational and drinking water reservoirs. Reservoirs have been increasing worldwide, highlighting the importance of understanding their biogeochemical processes. Dissolved organic matter (DOM) is a reactive and readily available source of nitrogen (N) and carbon (C) for microbes in aquatic systems, however, the relationships between DOM and cyanoHABs remain relatively unexplored in agricultural reservoirs. Our primary objective is to determine if an increase in allochthonous DOM leads to an increase in autochthonous DOM during a summer cyanobacterial bloom event in a warm monomictic agricultural reservoir. Water samples were collected two to three times per week from June 21st until October 5th, 2018 and analyzed for algal biomass and community composition, DOM quality and quantity. A variety of spectral parameters were used to determine DOM quality. One cyanobacterial bloom event was detected on July 16th. Maximum microcystin concentration for the sampling period was 0.68 [mu]gL-1 which is well under the EPA recommended recreational limit (8 [mu]gL-1). Dissolved organic carbon (DOC) concentrations were positively correlated with high amounts of terrestrial DOM. DOC concentrations and a350 also correlated positively with microcystin concentrations. Specific UV absorbance at 254nm (SUVA254) correlated positively with Chl-a (r=0.37, p=0.033). Our findings indicate that high DOM quantity has a significant relationship to microcystin concentration, which has negative implications for recreation and drinking water quality.Kyra M. Flora, Ruchi Bhattacharya, and Rebecca L. North (School of Natural Resources, University of Missouri, Columbia

Negative discrete moments of the derivative of the Riemann zeta-function

We obtain conditional upper bounds for negative discrete moments of the derivative of the Riemann zeta-function averaged over a subfamily of zeros of the zeta function which is expected to have full density inside the set of all zeros. For $k\leq 1/2$, our bounds for the $2k$-th moments are expected to be almost optimal. Assuming a conjecture about the maximum size of the argument of the zeta function on the critical line, we obtain upper bounds for these negative moments of the same strength while summing over a larger subfamily of zeta zeros.Comment: 19 page