Skip to content
DraconiticResearch
Search Sources API
190,851 studies31 sourcesUpdated 48 min ago
PreprintCC BY 4.0arXiv

Sharp unconditional moment bounds for products of L-functions

  • Markus Valås Hagen
Open at sourcePDFDOICite

Abstract

We investigate the mixed moments of products of irreducible GL(1) and GL(2) L-functions on the critical line, and establish sharp moment bounds for these quantities. In particular this establishes the order of these mixed moments in certain ranges. This determines unconditionally, for the first time, the order of magnitude of the first moment of cubic Dedekind zeta functions with negative discriminant. The proof of the lower bound introduces a new method for computing mixed moments, that is a mix of the classical method of Heath--Brown with the modern machinery of Harper, Heap, Radziwill, and Soundararajan.

Related

  1. Berry-Esseen bounds for products of random matrices under a 2+δ polynomial moment
    Zhi-Jun Cai, Qi-Man Shao, Hui Xiao +1
    arXivPreprintarXiv licenceFull textProbabilityarXiv
  2. Sharp upper bounds for Steklov eigenvalues on warped products
    Jade Brisson, Bruno Colbois, Alexandre Girouard +2
    arXivPreprintarXiv licenceFull textAnalysis & PDEsGeometry & topologyarXiv
  3. Sharp Fourth-Moment Wasserstein CLT Bounds
    Xiao Fang, Zi-Yao Su, Jiaxue Wang +1
    arXivPreprintarXiv licenceFull textProbabilityarXiv
  4. Sharp lower bounds for shifted moments of Dedekind zeta functions
    Benjamin Durkan, Nilmoni Karak, Kamalakshya Mahatab
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. Sharp Volume-Based Bounds for BMO Functions on Compact Domains and Applications
    Marin Mišur
    arXivPreprintCC BY-NC-ND 4.0Full textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{hagen2026sharp,
  title = {{Sharp unconditional moment bounds for products of L-functions}},
  author = {Markus Valås Hagen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11619},
  eprint = {2609.11619},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11619},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Sharp unconditional moment bounds for products of L-functions
AU  - Markus Valås Hagen
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11619
UR  - https://arxiv.org/abs/2609.11619
AB  - We investigate the mixed moments of products of irreducible GL(1) and GL(2) L-functions on the critical line, and establish sharp moment bounds for these quantities. In particular this establishes the order of these mixed moments in certain ranges. This determines unconditionally, for the first time, the order of magnitude of the first moment of cubic Dedekind zeta functions with negative discriminant. The proof of the lower bound introduces a new method for computing mixed moments, that is a mix of the classical method of Heath--Brown with the modern machinery of Harper, Heap, Radziwill, and Soundararajan.
ER  -