English

Near Counterexamples to Weil's Converse Theorem

Number Theory 2019-12-18 v2

Abstract

We show that in Weil's converse theorem the functional equations of multiplicative twists for at least the first p243\sqrt{\frac{p-24}{3}} moduli are needed in order to prove the modularity for Γ0(p)\Gamma_0(p).

Cite

@article{arxiv.1606.06923,
  title  = {Near Counterexamples to Weil's Converse Theorem},
  author = {Raphael S. Steiner},
  journal= {arXiv preprint arXiv:1606.06923},
  year   = {2019}
}

Comments

6 pages

R2 v1 2026-06-22T14:31:36.244Z