On a Gross conjecture over imaginary quadratic fields

Saad El Boukhari

On a Gross conjecture over imaginary quadratic fields

Number Theory 2023-02-09 v1

Authors: Saad El Boukhari

Abstract

Let $k$ be an imaginary quadratic number field, and $F/k$ a finite abelian extension of Galois group $G$ . We show that a Gross conjecture concerning the leading terms of Artin $L$ -series holds for $F/k$ and all rational primes which are split in $k$ and which do not divide $6$ .

Keywords

conjectures and proofs galois theory class number of quadratic fields

Cite

@article{arxiv.2302.04049,
  title  = {On a Gross conjecture over imaginary quadratic fields},
  author = {Saad El Boukhari},
  journal= {arXiv preprint arXiv:2302.04049},
  year   = {2023}
}

Comments

17 pages

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