High moments of the Riemann zeta-function

The authors describe a general approach which, in principal, should produce the correct (conjectural) formula for every even integer moment of the Riemann zeta function. They carry it out for the sixth and eigth powers; in the case of sixth powers this leads to the formula conjectured by Conrey and Ghosh, and in the case of eighth powers is new.Comment: Abstract added in migratio

Complexities of Chronic Opioid Exposure

Studies on repeated exposure to opioids have been carried out for decades yet the mechanisms for certain phenomena such as tolerance are still not fully understood. Furthermore, different medications, such as frequently prescribed benzodiazepines, or different disease states, such as HIV, have their own effects and interactions with chronic opioid exposure that are not fully understood. The overall objective of this dissertation was to investigate the complexities of chronic opioid exposure and how different disease states and medications may modulate the effects of chronic opioids. Our findings demonstrate that the administration of diazepam, at doses that are not antinociceptive or have any motor effects, reverse both antinociceptive and locomotor tolerance to orally active opioids. These doses of diazepam did not potentiate the acute effects of these prescription opioids. We also found that HIV-1 Tat expression significantly attenuated the antinociceptive potency of acute morphine in non-tolerant mice while not significantly altering the antinociceptive tolerance to morphine. Consistent with this, Tat attenuated withdrawal symptoms among morphine-tolerant mice. Pretreatment with maraviroc, a CCR5 antagonist blocked the effects of Tat, reinstating morphine potency in non-tolerant mice and restoring withdrawal symptomology in morphine-tolerant mice. Protein array analyses revealed only minor changes to cytokine profiles whether morphine was administered acutely or repeatedly; however, 24 h post repeated morphine administration, the expression of several cytokines was greatly increased. Tat further elevated levels of several cytokines and maraviroc pretreatment attenuated these effects. With the understanding that gap junctions may be involved in both HIV-Tat effects on opioid antinociception as well as tolerance, we investigated the role of gap junctions in opioid antinociceptive tolerance. We observed that carbenoxolone, a gap junction inhibitor, administered systemically attenuated the development of opioid antinociceptive tolerance. Furthermore, we observed a small percentage of carbenoxolone in brain tissue compared to the amount found in blood, suggesting a peripheral site of action. Finally, we show preliminary evidence that in vivo administration of carbenoxolone is able to attenuate tolerance to morphine in DRG neurons