Iwasawa invariants of sharp/flat $2$-adic L-functions for quadratic twists of elliptic curves

@misc{adachi2026iwasawa,
  title = {{Iwasawa invariants of sharp/flat $2$-adic $L$-functions for quadratic twists of elliptic curves}},
  author = {Taiga Adachi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.05305},
  eprint = {2607.05305},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.05305},
}

TY  - UNPB
TI  - Iwasawa invariants of sharp/flat $2$-adic L-functions for quadratic twists of elliptic curves
AU  - Taiga Adachi
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2607.05305
UR  - https://arxiv.org/abs/2607.05305
AB  - The aim of this paper is to study the variation under quadratic twists of the analytic Iwasawa invariants of Sprung's sharp/flat 2-adic L-functions for elliptic curves over ℚ with good supersingular reduction at $2$. Under the hypothesis that the μ-invariant vanishes, we obtain an explicit formula for the sharp/flat λ-invariants. This formula gives a supersingular analogue of Matsuno's formula in the good ordinary case. As an application, we show that the sharp/flat λ-invariants can be made arbitrarily large even among quadratic twists by single primes. Moreover, using the method of Hatley-Ray, we obtain an asymptotic lower bound for the number of quadratic twists with a prescribed sharp/flat 2-adic Iwasawa λ-invariant.
ER  -