Non-vanishing of Cubic Dirichlet L-Functions over the Eisenstein Field

Ahmet Muhtar Güloğlu

Non-vanishing of Cubic Dirichlet L-Functions over the Eisenstein Field

Number Theory 2023-06-27 v2

Authors: Ahmet Muhtar Güloğlu

Abstract

We establish an asymptotic formula for the first moment and derive an upper bound for the second moment of L-functions associated with the complete family of primitive cubic Dirichlet characters defined over the Eisenstein field. Our results are unconditional, and indicate that there are infinitely many characters within this family for which the L-function $L(s,\chi)$ does not vanish at the central point $s=1/2$ .

Keywords

cubic dirichlet l-functions eisenstein field primitive characters first moment second moment non-vanishing central point

Cite

@article{arxiv.2306.09474,
  title  = {Non-vanishing of Cubic Dirichlet L-Functions over the Eisenstein Field},
  author = {Ahmet Muhtar Güloğlu},
  journal= {arXiv preprint arXiv:2306.09474},
  year   = {2023}
}

Comments

arXiv admin note: text overlap with arXiv:2301.10979

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