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We determine the possible primes that can produce Eisenstein congruences. We provide several examples of Eisenstein congruences to substantiate our method. Ribet conjectured (\cite[p. 360]{MR3540618}) about these congruences for the square-free level $N$. Yoo proved the conjecture. For general $N$, Yoo proved a generalization of the conjecture, under some hypotheses, provided that those ideals are {\it rational}. We show that the generalization of Ribet's conjecture for certain non-square-free levels $N$ is true even for {\it non-rational} Eisenstein maximal ideals.
From: Dipramit Majumdar [view email]
[v1]
Mon, 15 Nov 2021 13:52:11 UTC (63 KB)
[v2]
Fri, 4 Feb 2022 13:59:00 UTC (66 KB)
[v3]
Thu, 25 Jun 2026 09:26:13 UTC (72 KB)
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