English

Joint distribution of Hecke eigenforms

Number Theory 2026-04-01 v2

Abstract

In this paper, we formulate conjectures on the joint distribution of several Hecke eigenforms. We prove an asymptotic formula of the joint mass of two Hecke eigenforms under the generalized Riemann Hypothesis (GRH) and the generalized Ramanujan conjecture (GRC). We also show that a higher decorrelation of two Hecke eigenforms asymptotically vanishes under GRH. As a consequence, we prove an asymptotic formula for the first moment of the triple product LL-functions under GRH and GRC.

Cite

@article{arxiv.2406.03073,
  title  = {Joint distribution of Hecke eigenforms},
  author = {Bingrong Huang},
  journal= {arXiv preprint arXiv:2406.03073},
  year   = {2026}
}

Comments

23 pages. To appear in IMRN. Comments welcome

R2 v1 2026-06-28T16:54:12.984Z