Average bounds for the $$ell $$ℓ-torsion in class groups of cyclic extensions
Average bounds for the $$ell $$ℓ-torsion in class groups of cyclic extensions
复制标题
循环扩展类组中 $$ell $$ℓ 扭转的平均界限
DOI：
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发表时间：
2017
影响因子：
0.8
通讯作者：
Martin Widmer
中科院分区：
文献类型：
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作者：
C. Frei;Martin Widmer
对于所有正整数$$ell$$ℓ，我们证明了K的类群中的$$ell$$ℓ-挠的非平凡界，它对某些任意大度的循环扩张族中的几乎所有数域K都成立。特别地，这样的界几乎对F的所有循环度-p-扩张都成立，其中F是任意数域，p是F与第p个割圆域线性不交的任何素数。在此过程中，我们证明了在有限多个素数上具有指定分裂行为的有界判别式场的精确渐近计数结果。
For all positive integers $$ell $$ℓ, we prove non-trivial bounds for the $$ell $$ℓ-torsion in the class group of K, which hold for almost all number fields K in certain families of cyclic extensions of arbitrarily large degree. In particular, such bounds hold for almost all cyclic degree-p-extensions of F, where F is an arbitrary number field and p is any prime for which F and the pth cyclotomic field are linearly disjoint. Along the way, we prove precise asymptotic counting results for the fields of bounded discriminant in our families with prescribed splitting behavior at finitely many primes.