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.
Title resolution pending
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
fields
math.NT 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Under the stated conditions on p and q, the Iwasawa λ-invariant of the cyclotomic ℤ₂-extension of K = ℚ(√(pq)) is zero.
citing papers explorer
-
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.
-
On the Iwasawa $\lambda$-invariant of the cyclotomic $\mathbb{Z}_2$-extension of a family of real quadratic fields in which $2$ splits
Under the stated conditions on p and q, the Iwasawa λ-invariant of the cyclotomic ℤ₂-extension of K = ℚ(√(pq)) is zero.