Congruences of $p$-adic $L$-functions of modular forms at non-ordinary primes
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| Format: | Preprint |
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2025
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| _version_ | 1866912536023007232 |
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| author | Corpuz, Raiza Lei, Antonio |
| author_facet | Corpuz, Raiza Lei, Antonio |
| contents | We present an analogue of Greenberg-Vatsal's and Emerton-Pollack-Weston's results on congruences of $p$-adic $L$-functions for $p$-non-ordinary cuspidal eigenforms $f$ and $g$ of equal weight that are $p$-congruent. In particular, we prove that the Iwasawa invariants of the analytic and algebraic signed $p$-adic $L$-functions of $f$ and $g$ are related by explicit formulae under appropriate hypotheses. We also show under the same assumptions that provided the algebraic and analytic $μ$-invariants vanish, the signed Iwasawa main conjecture is true for $f$ if and only if it is true for $g$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_09733 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Congruences of $p$-adic $L$-functions of modular forms at non-ordinary primes Corpuz, Raiza Lei, Antonio Number Theory 11F33 (Primary), 11F67, 11R23 (Secondary) We present an analogue of Greenberg-Vatsal's and Emerton-Pollack-Weston's results on congruences of $p$-adic $L$-functions for $p$-non-ordinary cuspidal eigenforms $f$ and $g$ of equal weight that are $p$-congruent. In particular, we prove that the Iwasawa invariants of the analytic and algebraic signed $p$-adic $L$-functions of $f$ and $g$ are related by explicit formulae under appropriate hypotheses. We also show under the same assumptions that provided the algebraic and analytic $μ$-invariants vanish, the signed Iwasawa main conjecture is true for $f$ if and only if it is true for $g$. |
| title | Congruences of $p$-adic $L$-functions of modular forms at non-ordinary primes |
| topic | Number Theory 11F33 (Primary), 11F67, 11R23 (Secondary) |
| url | https://arxiv.org/abs/2508.09733 |