On two conjectures of Gross for large vanishing orders

Hofer, Martin and Kleine, Sören (2021): On two conjectures of Gross for large vanishing orders. In: Monatshefte für Mathematik, Vol. 197, No. 1: pp. 85-109

Abstract

We prove the Gross order of vanishing conjecture in special cases where the vanishing order of the character in question can be arbitrarily large. In almost all previously known cases the vanishing order is zero or one. One major ingredient of our proofs is the equivalence of this conjecture to the Gross-Kuz'min conjecture. We present here a direct proof of this equivalence, using only the known validity of the Iwasawa Main Conjecture over totally real fields.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0026-9255
• Language: English