Arithmetic properties of similitude theta lifts from orthogonal to symplectic groups

DOI10.1007/s00229-013-0628-8zbMath1370.11053arXiv0902.4619OpenAlexW1978888747MaRDI QIDQ2248947

Tobias Berger

Publication date: 27 June 2014

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0902.4619

zbMATH Keywords

Siegel modular form\(p\)-integralitycohomological theta liftorthogonal symplectic group

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Theta series; Weil representation; theta correspondences (11F27)

Related Items (1)

Explicit inner product formulas and Bessel period formulas for HST lifts

Cites Work

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• Algebraic cycles on Shimura varieties of orthogonal type
• \(l\)-adic representations associated to modular forms over imaginary quadratic fields. I: Lifting to \(GSp_ 4(\mathbb{Q})\)
• Cycles in hyperbolic manifolds of non-compact type and Fourier coefficients of Siegel modular forms
• Arithmetic properties of the Shimura-Shintani-Waldspurger correspondence. With an appendix by Brian Conrad.
• Eisenstein series on Shimura varieties
• The theta correspondence and harmonic forms. I
• The theta correspondence and harmonic forms. II
• Eisenstein cohomology of arithmetic groups. The case \(GL_ 2\)
• Arithmétique des algèbres de quaternions
• Siegel's modular forms and the arithmetic of quadratic forms
• Galois representations associated to Siegel modular forms of low weight
• Arithmetic automorphic forms for the nonholomorphic discrete series of \(GSp(2)\)
• Fourier coefficients of modular forms of half integral weight, periods of modular forms and the special values of zeta functions
• The theta correspondence for similitudes
• Yoshida lifts and Selmer groups
• Congruence module for \(\text{GL}(2)\) of an imaginary quadratic field and Iwasawa theory of biquadratic CM field
• Critical values of the twisted tensor \(L\)-function in the imaginary quadratic case
• Yoshida lifts and the Bloch-Kato conjecture for the convolution \(L\)-function
• Integrality of a ratio of Petersson norms and level-lowering congruences
• Intersection numbers of cycles on locally symmetric spaces and Fourier coefficients of holomorphic modular forms in several complex variables
• On endoscopy and the refined Gross–Prasad conjecture for (SO₅, SO₄)
• On Siegel modular forms obtained form theta series.
• Langlands' Functoriality and the Weil Representation
• Siegel modular forms and theta series attached to quaternion algebras
• Tubes, Cohomology with Growth Conditions and an Application to the Theta Correspondence
• Periods of Cusp Forms and Elliptic Curves Over Imaginary Quadratic Fields
• Cycles with local coefficients for orthogonal groups and vector-valued Siegel modular forms
• Global \(L\)-packets for GSp(2) and theta lifts

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