For primes N and p with N ≡ 1 mod p, the rank r of Mazur's Eisenstein Hecke algebra equals one plus the vanishing order of a mod-p zeta element interpolating L-values at -1 when r is 2 or 3, with a uniform extension to level N² and partial results for higher ranks.
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The authors classify all finite group actions on cubic threefolds that make the threefold G-birationally rigid.
Explicit estimates for the count of integral ideals in number fields are derived with error terms that grow much more slowly with the degree n than the standard n^{n^2} bound.
citing papers explorer
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A new perspective on the rank of Mazur's Eisenstein Hecke algebra
For primes N and p with N ≡ 1 mod p, the rank r of Mazur's Eisenstein Hecke algebra equals one plus the vanishing order of a mod-p zeta element interpolating L-values at -1 when r is 2 or 3, with a uniform extension to level N² and partial results for higher ranks.
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G-birationally rigid cubic threefolds
The authors classify all finite group actions on cubic threefolds that make the threefold G-birationally rigid.
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Explicit counting of ideals in number fields of arbitrary degree
Explicit estimates for the count of integral ideals in number fields are derived with error terms that grow much more slowly with the degree n than the standard n^{n^2} bound.