Skip to content
DraconiticResearch
Search Sources API
185,139 studies31 sourcesUpdated 29 min ago
PreprintarXiv licencearXiv

Regularized spectral expansion of a Rankin--Selberg period and moments

  • Jakub Dobrowolski
  • Subhajit Jana
  • Ramon Nunes
Open at sourcePDFDOICite

Abstract

We establish a regularized spectral decomposition of the squared magnitude of a maximal degenerate Eisenstein series as a Schwartz distribution on GLn. Although the original problem is on GLn, its spectral components are described entirely by the automorphic spectrum of GL2. As an application, we prove a partial reciprocity formula relating the second moment of GLn×GLn Rankin--Selberg central L-values and a mixed moment of L-values of GL2. We also prove, assuming the generalized Ramanujan conjecture, an asymptotic formula for the second moment of the above Rankin--Selberg L-functions over a conductor-aspect family with an error term of square-root-cancellation strength.

Related

  1. Weyl Bounds for GL2× GL2 Rankin--Selberg L-functions via Short Spectral Moments
    Zihao Wang
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Archimedean Modular Symbols for Rankin-Selberg Convolutions of GLn(ℂ)×GLn(ℂ) and GLn(ℂ)×GLn+1(ℂ)
    Yubo Jin, Zeyu Tian
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. Rankin--Selberg integrals of opposite conductor--one newforms
    Dongwen Liu, Lei Zhang
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  4. Nonlinear twists of Rankin-Selberg coefficients in the eigenvalue aspect
    Yangbo Ye
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Spectral moments and characteristic polynomials of vertex expansion hypergraphs of graphs
    Ge Lin, Changjiang Bu
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{dobrowolski2026regularized,
  title = {{Regularized spectral expansion of a Rankin--Selberg period and moments}},
  author = {Jakub Dobrowolski and Subhajit Jana and Ramon Nunes},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.01358},
  eprint = {2609.01358},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01358},
}
RIS
TY  - UNPB
TI  - Regularized spectral expansion of a Rankin--Selberg period and moments
AU  - Jakub Dobrowolski
AU  - Subhajit Jana
AU  - Ramon Nunes
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.01358
UR  - https://arxiv.org/abs/2609.01358
AB  - We establish a regularized spectral decomposition of the squared magnitude of a maximal degenerate Eisenstein series as a Schwartz distribution on GL_n. Although the original problem is on GL_n, its spectral components are described entirely by the automorphic spectrum of GL_2. As an application, we prove a partial reciprocity formula relating the second moment of GL_n×GL_n Rankin--Selberg central L-values and a mixed moment of L-values of GL_2. We also prove, assuming the generalized Ramanujan conjecture, an asymptotic formula for the second moment of the above Rankin--Selberg L-functions over a conductor-aspect family with an error term of square-root-cancellation strength.
ER  -