比利时vs摩洛哥足彩
,
university of california san diego
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number theory seminar - math 209
christopher keyes
emory
local solubility in families of superelliptic curves
abstract:
if we choose at random an integral binary form $f(x, z)$ of fixed degree $d$, what is the probability that the superelliptic curve with equation $c \colon: y^m = f(x, z)$ has a $p$-adic point, or better, points everywhere locally? in joint work with lea beneish, we show that the proportion of forms $f(x, z)$ for which $c$ is everywhere locally soluble is positive, given by a product of local densities. by studying these local densities, we produce bounds which are suitable enough to pass to the large $d$ limit. in the specific case of curves of the form $y^3 = f(x, z)$ for a binary form of degree 6, we determine the probability of everywhere local solubility to be 96.94%, with the exact value given by an explicit infinite product of rational function expressions.
[pre-talk at 1:20pm]
december 1, 2022
2:00 pm
apm 6402 and zoom; see //www.ladysinger.com/~nts
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