Ramanujan graphs and exponential sums over function fields
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DOI: 10.1016/j.jnt.2020.05.010
Abstract: We prove that $q+1$-regular Morgenstern Ramanujan graphs $X^{q,g}$ (depending on $g\in\mathbb{F}_q[t]$) have diameter at most $\left(\frac{4}{3}+\varepsilon\right)\log_{q}|X^{q,g}|+O_{\varepsilon}(1)$ (at least for odd $q$ and irreducible $g$) provided that a twisted Linnik-Selberg conjecture over $\mathbb{F}_q(t)$ is true. This… read more here.
Keywords: sums function; ramanujan graphs; graphs exponential; exponential sums ... See more keywords