On the Iwasawa invariants of BDP Selmer groups and BDP P-adic L-fucntions

Let \(p\) be an odd prime. Let \(f_1\) and \(f_2\) be weight-two Hecke eigen-cuspforms with isomorphic residual Galois representations at \(p\). Greenberg--Vatsal and Emerton--Pollack--Weston showed that if \(p\) is a good ordinary prime for the two forms, the Iwasawa invariants of their \(p\)-prima...

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Bibliographic Details
Published in:arXiv.org 2023-08
Main Authors: Lei, Antonio, Müller, Katharina, Xia, Jiacheng
Format: Article
Language:English
Subjects:
Fields (mathematics)
Invariants
Number theory
Online Access:Get full text
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Summary:Let \(p\) be an odd prime. Let \(f_1\) and \(f_2\) be weight-two Hecke eigen-cuspforms with isomorphic residual Galois representations at \(p\). Greenberg--Vatsal and Emerton--Pollack--Weston showed that if \(p\) is a good ordinary prime for the two forms, the Iwasawa invariants of their \(p\)-primary Selmer groups and \(p\)-adic \(L\)-functions over the cyclotomic \(\mathbb{Z}_p\)-extension of \(\mathbb{Q}\) are closely related. The goal of this article is to generalize these results to the anticyclotomic setting. More precisely, let \(K\) be an imaginary quadratic field where \(p\) splits. Suppose that the generalized Heegner hypothesis holds with respect to both \((f_1,K)\) and \((f_2,K)\). We study relations between the Iwasawa invariants of the BDP Selmer groups and the BDP \(p\)-adic \(L\)-functions of \(f_1\) and \(f_2\).
ISSN:2331-8422