Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 20 min ago
PreprintarXiv licencearXiv

Jacquet-Zagier treatment of the beyond endoscopy trace formula for GL2

  • Pranjal Pandurang Warade
Open at sourcePDFDOICite

Abstract

We begin the study of the beyond endoscopic trace formula for GL2 over ℚ attached to any symmetric power representation σk of the dual group GL2(ℂ). For an adelic function that incorporates the L-functions L(sB,π,σk) through the basic functions at all the finite places, we integrate the cuspidal kernel against a corresponding Eisenstein series E(g,s) and realize the trace formula as a residue at s=1, replacing Arthur's truncation operation by a continuously deformed trace formula. We argue Poisson summation on the trace variable of the Hitchin-Steinberg base and show that the dominant term of the elliptic part admits meromorphic continuation to R(sB) ≥ 0 with a pole of order k at sB =1.

Related

  1. Relative Hitchin fibrations and endoscopy for Unitary Friedberg--Jacquet varieties
    Thomas Hameister, Spencer Leslie
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Zagier's 2-3-2 formula for multiple Eisenstein series
    Henrik Bachmann
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. A Kohnen-Zagier Formula in Level 1
    Clayton Williams
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  4. Integrability of conformal loop ensemble: imaginary DOZZ formula and beyond
    Morris Ang, Gefei Cai, Xin Sun +1
    Journal of the American Mathematical SocietyPeer-reviewedLicence not statedFull text71 citedMathematical physicsOpenAlex
  5. Beyond Tweedie's Formula: Conditional Score Modeling for Empirical Bayes Inference
    Shonosuke Sugasawa, Zhigen Zhao
    arXivPreprintarXiv licenceFull textStatisticsarXiv

Cite

BibTeXRIS
BibTeX
@misc{warade2026jacquetzagier,
  title = {{Jacquet-Zagier treatment of the beyond endoscopy trace formula for $\mathrmGL_2$}},
  author = {Pranjal Pandurang Warade},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.01990},
  eprint = {2609.01990},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01990},
}
RIS
TY  - UNPB
TI  - Jacquet-Zagier treatment of the beyond endoscopy trace formula for GL_2
AU  - Pranjal Pandurang Warade
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.01990
UR  - https://arxiv.org/abs/2609.01990
AB  - We begin the study of the beyond endoscopic trace formula for GL_2 over ℚ attached to any symmetric power representation σ_k of the dual group GL_2(ℂ). For an adelic function that incorporates the L-functions L(s_B,π,σ_k) through the basic functions at all the finite places, we integrate the cuspidal kernel against a corresponding Eisenstein series E(g,s) and realize the trace formula as a residue at s=1, replacing Arthur's truncation operation by a continuously deformed trace formula. We argue Poisson summation on the trace variable of the Hitchin-Steinberg base and show that the dominant term of the elliptic part admits meromorphic continuation to R(s_B) ≥ 0 with a pole of order k at s_B =1.
ER  -