On rr-gaps between zeros of the Riemann zeta-function

Under the Riemann Hypothesis, we prove for any natural number $r$ there exist infinitely many large natural numbers $n$ such that $(\gamma_{n+r}-\gamma_n)/(2\pi /\log \gamma_n) > r + \Theta\sqrt{r}$ and $(\gamma_{n+r}-\gamma_n)/(2\pi /\log \gamma_n) < r - \vartheta\sqrt{r}$ for explicit absolute positive constants $\Theta$ and $\vartheta$, where $\gamma$ denotes an ordinate of a zero of the Riemann zeta-function on the critical line. Selberg published announcements of this result several times but did not include a proof. We also suggest a general framework which might lead to stronger statements concerning the vertical distribution of nontrivial zeros of the Riemann zeta-function.Comment: to appear in the Bulletin of the London Mathematical Societ

Denise Knighton Retires After Almost 40 Years

UM associate registrar leaves legacy of dedicatio

Gold Nanoparticles: Core Conversion of Au144(SCH2CH2Ph)60 to Au99(SPh-CH3)42 Using Aromatic Thiolate Ligands and Crystallization of Au99(SPh-CH3)42

The purpose of this thesis is to synthesize Au144(SCH2CH2Ph)60 using a two-step synthesis reaction, and then using this product to conduct a core conversion from Au144(SCH2CH2Ph)60 to Au99(SPh-CH3)42. The Au99(SPh-CH3)42 product will then be used to attempt to form crystals using five different crystal set-up methods. Au144(SCH2CH2Ph)60 is made with aliphatic thiolate ligands, and when it is placed in a mixture containing excess para-methyl benzenethiol, it undergoes a core-conversion to Au99(SPh-CH3)42. This is a relatively new nanoparticle, and it is being used to hopefully form crystals which can, in turn, give information about its structure. The crystallization was unsuccessful with the five different set-ups employed, but the Au99(SPh-CH3)42 structure is still being studied with the hopeful crystal structure being found soon

Banning Books Threatens Freedom of Speech

UM librarian shares concerns about protecting diversity of opinion and perspectiv