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比利时vs摩洛哥足彩 ,
university of california san diego

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math 209 - number theory

djordjo milovic

leiden university

divisibility by 16 of class numbers in certain families of quadratic number fields

abstract:

the density of primes $p\equiv 1\pmod{8}$ (resp. $p\equiv 7\pmod{8}$) such that the class number of $\mathbb{q}(\sqrt{-p})$ (resp. $\mathbb{q}(\sqrt{-2p})$) is divisible by $2^{k+2}$ is conjectured to be $2^{-k}$ for all positive integers $k$. the conjecture has been resolved for $k = 1$ by the chebotarev density theorem. for the family of quadratic fields $\mathbb{q}(\sqrt{-2p})$, we use methods of friedlander and iwaniec to prove the conjecture for $k = 2$. moreover, we show that there are infinitely many primes $p$ for which the class number of $\mathbb{q}(\sqrt{-p})$ is divisible by $16$.

host: cristian popescu

january 15, 2015

1:00 pm

ap&m 7321

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