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PreprintCC BY 4.0arXiv

Hecke Eigenvalues of Ikeda Lifts

  • Nagarjuna Chary Addanki
  • Ameya Pitale
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Abstract

In this paper, we study the Hecke eigenvalues of Ikeda lifts. Using the spherical map for the Hecke algebra of the symplectic group, we obtain an explicit formula for the eigenvalues λF(pr). From this formula, we show that λF(pr) can be written as a polynomial in p± 1/2 with a positive leading term. Furthermore, we prove that the coefficients of this polynomial are bounded and, as a consequence, the Hecke eigenvalues λF(pr) are positive for all sufficiently large primes p.

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Cite

BibTeXRIS
BibTeX
@misc{addanki2026hecke,
  title = {{Hecke Eigenvalues of Ikeda Lifts}},
  author = {Nagarjuna Chary Addanki and Ameya Pitale},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.16083},
  eprint = {2605.16083},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.16083},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Hecke Eigenvalues of Ikeda Lifts
AU  - Nagarjuna Chary Addanki
AU  - Ameya Pitale
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2605.16083
UR  - https://arxiv.org/abs/2605.16083
AB  - In this paper, we study the Hecke eigenvalues of Ikeda lifts. Using the spherical map for the Hecke algebra of the symplectic group, we obtain an explicit formula for the eigenvalues λ_F(p^r). From this formula, we show that λ_F(p^r) can be written as a polynomial in p^± 1/2 with a positive leading term. Furthermore, we prove that the coefficients of this polynomial are bounded and, as a consequence, the Hecke eigenvalues λ_F(p^r) are positive for all sufficiently large primes p.
ER  -