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arXiv · 2503.00247

Congruent modular forms and anticyclotomic Iwasawa theory

Dac-Nhan-Tam Nguyen
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Abstract

Let $p$ be an odd prime. Consider normalized newforms $f_1,f_2$ that both satisfy the Heegner hypothesis for an imaginary quadratic field $K$ and suppose that they induce isomorphic residual Galois representations. In the work of Greenberg-Vatsal and Emerton-Pollack-Weston, the authors compare the cyclotomic Iwasawa $\mu$ and $\lambda$-invariants of $f_1$ and $f_2$. We extend this to the anticyclotomic indefinite setting by comparing the BDP $p$-adic $L$-functions attached to $f_1$ and $f_2$. Using this comparison, we obtain arithmetic implications for both generalized Heegner cycles and the Iwasawa main conjecture.

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Dac-Nhan-Tam Nguyen. 2025-02-28. Congruent modular forms and anticyclotomic Iwasawa theory. https://arxiv.org/abs/2503.00247

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