Fourier expansion of Arakawa lifting II: Relation with central L-values

DOI10.1142/S0129167X16500014zbMath1408.11029MaRDI QIDQ2790320

Hiro-aki Narita, Atsushi Murase

Publication date: 3 March 2016

Published in: International Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Fourier coefficientscentral \(L\)-valuestheta liftsquaternion unitary grouptoral integrals

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Other groups and their modular and automorphic forms (several variables) (11F55) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Fourier coefficients of automorphic forms (11F30)

Related Items (3)

A \(p\)-adic Waldspurger formula ⋮ Jacquet-Langlands-Shimizu correspondence for theta lifts to \(\mathrm{GSp}(2)\) and its inner forms II: an explicit formula for Bessel periods and the non-vanishing of theta lifts ⋮ Refined global Gross-Prasad conjecture on special Bessel periods and Böcherer's conjecture

Cites Work

• Fourier-Jacobi expansion of automorphic forms on \(\text{Sp}(1,q)\) generating quaternionic discrete series
• Sur les coefficients de Fourier des formes modulaires de poids demi-entier
• Jacquet-Langlands-Shimizu correspondence for theta lifts to \(\mathrm{GSp}(2)\) and its inner forms I: an explicit functorial correspondence
• Fourier expansion of Arakawa lifting. I: An explicit formula and examples of non-vanishing lifts
• Automorphic forms on GL (2)
• Automorphic forms on \(\mathrm{GL}(2)\). Part II
• Positivity of quadratic base change $L$-functions
• Über die Darstellbarkeit von Modulformen durch Thetareihen.
• Quadratische Formen und Modulfunktionen
• Central values of Rankin L-functions
• On quaternionic discrete series representations, and their continuations.
• A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$
• On central critical values of the degree four 𝐿-functions for GSp(4): the fundamental lemma
• On central critical values of the degree four $L$-functions for $\mathrm {GSp}(4)$: The fundamental lemma. III
• Central L-Values and Toric Periods for GL(2)
• Problems in the theory of automorphic forms to Salomon Bochner in gratitude
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