On Shimura, Shintani and Eichler-Zagier correspondences

DOI10.1090/S0002-9947-00-02423-5zbMath0985.11020OpenAlexW1901582082MaRDI QIDQ4955700

Murugesan Manickam, B. Ramakrishnan

Publication date: 22 May 2000

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-00-02423-5

zbMATH Keywords

Jacobi formsPoincaré seriesnewformsShimura correspondenceJacobi cusp formsShintani correspondenceEichler-Zagier correspondencehalf-integral weight newformsJacobi newforms

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Holomorphic modular forms of integral weight (11F11) Jacobi forms (11F50) Modular correspondences, etc. (11F32)

Related Items (28)

On classical Saito-Kurokawa liftings ⋮ An inner product relation on Saito-Kurokawa lifts ⋮ On the non-vanishing of Jacobi Poincaré series ⋮ On newforms of half-integral weight and Jacobi forms ⋮ Trace formula for Jacobi forms of odd squarefree level ⋮ \(\Lambda\)-adic families of Jacobi forms ⋮ On the analogue of Weil's converse theorem for Jacobi forms and their lift to half-integral weight modular forms ⋮ ON FUNDAMENTAL FOURIER COEFFICIENTS OF SIEGEL CUSP FORMS OF DEGREE 2 ⋮ Jacobi forms, Saito-Kurokawa lifts, their pullbacks and sup-norms on average ⋮ Class numbers, cyclic simple groups, and arithmetic ⋮ Non-vanishing of theta components of Jacobi forms with level and an application ⋮ Hermitian Maass lift for general level ⋮ On the first Fourier-Jacobi coefficient of Siegel modular forms of degree two ⋮ REPRESENTATIONS OF BINARY FORMS BY QUATERNARY FORMS ⋮ On the Bloch-Kato conjecture for elliptic modular forms of square-free level ⋮ Level lowering for half-integral weight modular forms ⋮ Saito-Kurokawa lifts of square-free level ⋮ Shintani and Shimura lifts of cusp forms on certain arithmetic groups and their applications ⋮ ON A CORRESPONDENCE BETWEEN JACOBI CUSP FORMS AND ELLIPTIC CUSP FORMS ⋮ A canonical subspace of modular forms of half-integral weight ⋮ On the Fourier coefficients of modular forms of half integral weight belonging to Kohnen's spaces and the critical values of zeta functions ⋮ An estimate for a certain average of the special values of character twists of modular $L$-functions ⋮ An Eichler-Zagier map for Jacobi cusp forms on \(\mathcal{H} \times \mathbb{C}^{(g, 1)}\) ⋮ Mixed-level Saito-Kurokawa liftings ⋮ Level aspect of simultaneous nonvanishing for the central 𝐿-values associated to cusp forms ⋮ Analytic number theory in India during 2001-2010 ⋮ Unnamed Item ⋮ Pullbacks of Saito-Kurokawa lifts and a central value formula for degree 6 \(L\)-series

Cites Work

• The theory of Jacobi forms
• Fourier coefficients and modular forms of half-integral weight
• On the theory of newforms of half-integral weight
• Fourier coefficients of modular forms of half-integral weight
• Heegner points and derivatives of \(L\)-series. II
• Jacobi forms and a certain space of modular forms
• The decomposition of the spaces of cusp forms of half-integral weight and trace formula of Hecke operators
• Sur les coefficients de Fourier des formes modulaires de poids demi-entier
• Values of L-series of modular forms at the center of the critical strip
• On Shintani correspondence
• On Saito-Kurokawa descent for congruence subgroups
• Newforms and functional equations
• Hecke operators on \(\Gamma_0(m)\)
• On modular forms of half integral weight
• Newforms of half-integral weight.
• On construction of holomorphic cusp forms of half integral weight
• On twisting operators and newforms of half-integral weight
• Unnamed Item
• Unnamed Item

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