Critical values of the twisted tensor \(L\)-function in the imaginary quadratic case

DOI10.1215/S0012-7094-99-09619-9zbMath0983.11024OpenAlexW1976662252MaRDI QIDQ1974892

Eknath P. Ghate

Publication date: 27 March 2000

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-99-09619-9

zbMATH Keywords

critical valuesRankin-Selberg methodmotivic \(L\)-functionsDeligne's conjecturestwisted tensor \(L\)-functionEichler-Shimura-Harden isomorphism

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66)

Related Items (11)

Theta lifts of Bianchi modular forms and applications to paramodularity ⋮ Explicit inner product formulas and Bessel period formulas for HST lifts ⋮ ARITHMETIC OFp‐IRREGULAR MODULAR FORMS: FAMILIES ANDp‐ADICL‐FUNCTIONS ⋮ \(p\)-adic Asai \(L\)-functions of Bianchi modular forms ⋮ \(\mathfrak{p}\)-adic distributions attached to twisted tensor \(L\)-functions for \(\mathrm{GL}_{2}\) over CM fields ⋮ Arithmetic properties of similitude theta lifts from orthogonal to symplectic groups ⋮ Pullback formulae for nearly holomorphic Saito-Kurokawa lifts ⋮ On Fourier coefficients of Niebur Poincaré series ⋮ Functional equation of the \(p\)-adic \(L\)-function of Bianchi modular forms ⋮ Arithmetic Aspects of Bianchi Groups ⋮ A construction of \(p\)-adic Asai \(L\)-functions for \(\mathrm{GL}_2\) over CM fields

Cites Work

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• Eisenstein cohomology of arithmetic groups. The case \(GL_ 2\)
• On the Ramanujan conjecture and finiteness of poles for certain \(L\)-functions
• On certain zeta functions attached to two Hilbert modular forms. II: The case of automorphic forms on a quaternion algebra
• \(p\)-ordinary cohomology groups for \(\text{SL}(2)\) over number fields
• On certain Dirichlet series associated with Hilbert modular forms and Rankin's method
• On zeroes of the twisted tensor \(L\)-function
• Certain Dirichlet series attached to automorphic forms over imaginary quadratic fields
• On the critical values of \(L\)-functions of \(GL(2)\) and \(GL(2)\times GL(2)\)
• Twisted tensors and Euler products

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