$L$-functions at the origin and annihilation of class groups in multiquadratic extensions
$L$-functions at the origin and annihilation of class groups in multiquadratic extensions
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$L$-在多重二次扩张中类群的原点和湮灭处的函数
DOI：
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发表时间：
2012
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通讯作者：
J. Sands
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文献类型：
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作者：
J. Sands
固定数域的伽罗华扩张K/F，使得伽罗华群G的指数为2.设S是F的有限素数集，包含无穷个素数和在K中分支的所有素数，SK表示K中位于S中的素数之上的素数，OS K表示K的SK-整数环.我们从K/F的等变L函数θS K/F(S)和集合S得到了OS K类群的非平凡零化子，而不考虑在原点消失的次序.
Fix a Galois extension K/F of number fields such that the Galois group G has exponent 2. Let S be a finite set of primes of F containing the infinite primes and all those which ramify in K, let SK denote the primes of K lying above those in S, and let OS K denote the ring of SK-integers of K. We obtain non-trivial annihilators for the class group of OS K from the equivariant L-function θS K/F (s) for K/F and the set S, regardless of the order of vanishing at the origin.