On the Kuznetsov trace formula for \(\operatorname{PGL}_2(\mathbb{C})\)

DOI10.1016/j.jfa.2017.01.011zbMath1361.11036arXiv1606.02477OpenAlexW2583629385MaRDI QIDQ517097

Zhi Qi

Publication date: 16 March 2017

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.02477

zbMATH Keywords

Kloosterman sumspectral decompositionBessel functionautomorphic formWhittaker functionKuznetsov trace formulaBruhat coordinates

Mathematics Subject Classification ID

Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items

Hecke-Maass cusp forms on \(\operatorname{PGL}_n\) of large levels with non-vanishing \(L\)-values ⋮ On the Fourier transform of Bessel functions over complex numbers. I: The spherical case ⋮ A Vorono\xEF–Oppenheim summation formula for number fields ⋮ Bessel identities in the Waldspurger correspondence over the complex numbers ⋮ On the Fourier transform of Bessel functions over complex numbers—II: The general case ⋮ Theory of Fundamental Bessel Functions of High Rank ⋮ A Whittaker-Plancherel inversion formula for \(\mathrm{SL}_2(\mathbb{C} )\) ⋮ Subconvexity for twisted 𝐿-functions on 𝐺𝐿₃ over the Gaussian number field

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Kuznetsov formulas for real rank one groups
• Fourier coefficients of automorphic forms
• Summation formulas for general Kloosterman sums
• Kloosterman sums and Fourier coefficients of cusp forms
• The multiplicity one theorem for \(\mathrm{GL}_n\)
• On the functional equations satisfied by Eisenstein series
• Fourier coefficients of cusp forms
• Sum formula for \(SL_2\) over a number field and Selberg type estimates for exceptional eigenvalues
• Sum formula for Kloosterman sums and fourth moment of the Dedekind zeta-function over the Gaussian number field
• Automorphic forms on semisimple Lie groups. Notes by J. G. M. Mars.
• Automorphic forms on GL (2)
• A SEMI-ADELIC KUZNETSOV FORMULA OVER NUMBER FIELDS
• PETERSSON'S CONJECTURE FOR CUSP FORMS OF WEIGHT ZERO AND LINNIK'S CONJECTURE. SUMS OF KLOOSTERMAN SUMS