Rankin-Selberg method for Siegel cusp forms

DOI10.1017/S0027763000003226zbMath0715.11025OpenAlexW1527788479MaRDI QIDQ3202178

Tadashi Yamazaki

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1017/s0027763000003226

zbMATH Keywords

functional equationJacobi formsDirichlet seriesmeromorphic continuationFourier-Jacobi coefficientsRankin convolutionSiegel cusp formsintegral representation of Rankin-Selberg type

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66)

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A note on mass equidistribution of holomorphic Siegel modular forms ⋮ Characteristic twists of a Dirichlet series for Siegel cusp forms ⋮ Certain series attached to an even number of elliptic modular forms ⋮ Ikeda's conjecture on the period of the Duke–Imamoḡlu–Ikeda lift ⋮ Estimates for Fourier coefficients of Hermitian cusp forms of degree two ⋮ Equidistribution rates, closed string amplitudes, and the Riemann hypothesis ⋮ Additive twists of \(L^2\)-norm of Fourier-Jacobi coefficients of Siegel cusp forms ⋮ Certain L-series of Rankin-Selberg type associated to Siegel modular forms of degree \(g\) ⋮ On the oscillatory behavior of certain arithmetic functions associated with automorphic forms ⋮ Quotients of L-functions ⋮ On Dirichlet series and Petersson products for Siegel modular forms ⋮ RANKIN-SELBERG METHOD FOR JACOBI FORMS OF INTEGRAL WEIGHT AND OF HALF-INTEGRAL WEIGHT ON SYMPLECTIC GROUPS ⋮ A certain Dirichlet series of Rankin-Selberg type associated with the Ikeda lifting ⋮ A Dirichlet series attached to three Siegel modular forms ⋮ Estimates for Fourier coefficients of Siegel cusp forms ⋮ Estimates for Fourier coefficients of Siegel cusp forms ⋮ Petersson norms of not necessarily cuspidal Jacobi modular forms and applications ⋮ Non-vanishing of Miyawaki type lifts ⋮ Ramanujan–Petersson conjecture for Fourier–Jacobi coefficients of Siegel cusp forms ⋮ On the Petersson inner products of Fourier–Jacobi coefficients and Hecke eigenvalues of Siegel cusp forms

Cites Work

• A certain Dirichlet series attached to Siegel modular forms of degree two
• EISENSTEIN SERIES ON THE SYMPLECTIC GROUP