3 problems

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The minimal-intersection conjecture for graphs of Hecke operators
Minimal-intersection conjecture. The lower bound is always attained for graphs of Hecke operators; equivalently, the intersection of $\operatorname{im}(M-\lambda)$ and…
Conjectureopeneigenforms graph-theory hecke-operatorsarXiv posted 2 days ago
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The characterization of vanishing Hecke-obstruction quantity for mod- \ell eigenforms
Vanishing characterization conjecture.
Conjectureopencongruences eigenforms modular-formsarXiv posted 2 days ago
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Finiteness conjecture for congruence classes of strong eigenforms modulo $p^n$
Finiteness conjecture for strong eigenforms. There are only finitely many congruence classes of strong eigenforms modulo $p^n$ for any $n$ .
Conjectureopeneigenforms modular-forms p-adic-modular-formsarXiv posted 2 days ago

The minimal-intersection conjecture for graphs of Hecke operators