A quantum probabilistic approach to Hecke algebras for 𝔭-adic PGL2

DOI10.1142/S0219025718500157zbMath1448.46052arXiv1803.02217OpenAlexW3098330329MaRDI QIDQ4554054

Shingo Sugiyama, Seiken Saito, Takehiro Hasegawa, Hayato Saigo

Publication date: 7 November 2018

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.02217

zbMATH Keywords

quantum probabilityspherical Hecke algebrasFourier inversion formulas

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Noncommutative probability and statistics (46L53) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items (1)

The limit theorem with respect to the matrices on non-backtracking paths of a graph

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Regularized periods of automorphic forms on \(\mathrm{GL}(2)\)
• The arcsine law and an asymptotic behavior of orthogonal polynomials
• A family of Calabi-Yau varieties and potential automorphy. II.
• Averages of central \(L\)-values of Hilbert modular forms with an application to subconvexity
• The Sato-Tate conjecture for modular forms of weight 3
• Quantum probability and spectral analysis of graphs. With a foreword by Professor Luigi Accardi.
• A family of Calabi-Yau varieties and potential automorphy
• Harmonic analysis of spherical functions on reductive groups over p-adic fields
• An explicit trace formula of Jacquet-Zagier type for Hilbert modular forms
• Asymptotic behaviors of means of central values of automorphic \(L\)-functions for \(\mathrm{GL}(2)\)
• Orbital integrals on unitary hyperbolic spaces over \(\mathfrak p\)-adic fields
• Average values of modular \(L\)-series via the relative trace formula
• Relative trace formulas and subconvexity estimates for $L$-functions of Hilbert modular forms
• Spectral Analysis of Growing Graphs
• Existence of Hilbert Cusp Forms with Non-vanishingL-values
• Spherical Functions Over B-Adic Fields, I
• Interacting Fock Spaces and Gaussianization of Probability Measures
• A NEW LOOK AT THE ARCSINE LAW AND "QUANTUM-CLASSICAL CORRESPONDENCE"
• Spectral means of central values of automorphic 𝐿-functions for 𝐺𝐿(2)
• Répartition asymptotique des valeurs propres de l’opérateur de Hecke 𝑇_𝑝

This page was built for publication: A quantum probabilistic approach to Hecke algebras for 𝔭-adic PGL2