On the μ-invariant of two-variable 2-adic L-functions

被引:0
作者
Li, Yong-Xiong [1 ]
机构
[1] Yanqi Lake Beijing Inst Math Sci & Applicat, Beijing, Peoples R China
关键词
Elliptic curves; Iwasawa theory; mu-invariant; ADIC L-FUNCTIONS; ELLIPTIC-CURVES; IWASAWA THEORY; CONJECTURE; VALUES;
D O I
10.1017/S0017089525000035
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let K = Q(root-7) and O the ring of integers in K. The prime 2 splits in K, say 2O = p center dot p*. Let A be an elliptic curve defined over K with complex multiplication by O. Assume that A has good ordinary reduction at both p and p*. Write K-infinity for the field generated by the 2(infinity)-division points of A over K and let G = Gal(K-infinity/K). In this paper, by adopting a congruence formula of Yager and De Shalit, we construct the two-variable 2-adic L-function on G. Then by generalizing De Shalit's local structure theorem to the two-variable setting, we prove a two-variable elliptic analogue of Iwasawa's theorem on cyclotomic fields. As an application, we prove that every branch of the two-variable measure has Iwasawa mu invariant zero.
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页数:31
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