Weak Siegel-Weil formula for 𝕄₂(ℚ) and arithmetic on quaternions

DOI10.1090/tran/8324zbMath1475.11213arXiv1804.05247OpenAlexW3103469827MaRDI QIDQ5857745

Tuoping Du

Publication date: 7 April 2021

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.05247

zbMATH Keywords

Eisenstein seriesHecke correspondenceWhittaker functionsSiegel-Weil formulatheta integrals

Mathematics Subject Classification ID

Integral representations (11S23) Arithmetic aspects of modular and Shimura varieties (11G18) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41) Modular correspondences, etc. (11F32) Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Cites Work

• Quaternions and Kudla's matching principle
• The regularized Siegel-Weil formula (the second term identity) and the Rallis inner product formula
• Eisenstein series for \(\mathrm{SL}(2)\)
• \(L\)-functions and the oscillator representation
• The theta correspondence and harmonic forms. II
• Values of certain Whittaker functions on a p-adic reductive group
• Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus
• Splitting metaplectic covers of dual reductive pairs
• A regularized Siegel-Weil formula: The first term identity
• Sur la formule de Siegel dans la théorie des groupes classiques
• Sur certains groupes d'opérateurs unitaires
• On the Weil-Siegel formula II.
• Quaternion Orders, Quadratic Forms, and Shimura Curves
• Modular Forms and Special Cycles on Shimura Curves. (AM-161)
• On the Representations of a Number as the Sum of Three Squares
• Modular Forms
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