Anti-cyclotomic Katz $p$-adic $L$-functions and congruence modules
Anti-cyclotomic Katz $p$-adic $L$-functions and congruence modules
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反分环 Katz $p$-adic $L$-函数和同余模块
DOI：
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
J. Tilouine
中科院分区：
文献类型：
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作者：
H. Hida;J. Tilouine
- 证明了希达/？-的同余模的特征幂级数的整除性通过具有辅助导体的Katz ^-adic L-函数的反分圆特化，来自CM-场（具有固定的CM-类型）的theta级数的adic族。这需要首先构造这个^-adic L-函数，因为在Katz的原始论文中，辅助导体是平凡的。这里证明的整除性是两个步骤之一，两个整除性预测的（反分圆）岩泽主要猜想CM领域。第二步已由作者完成，并将在其他地方发表。
— The purpose of this paper is to prove the divisibility of the characteristic power series of the congruence module of a Hida /?-adic family of theta series coming from a CM-field (with fixed CM-type) by the anti-cyclotomic specialisation of the Katz ^-adic L-function with auxiliary conductor. This requires to construct first this^-adic L-function since in the original paper by Katz the auxiliary conductor was trivial. The divisibility proven here is one of two steps towards one of the two divisibilities predicted by the (anti-cyclotomic) Iwasawa main conjecture for CM-fields. The second step has been carried out by the authors and will be published elsewhere.