Displaying similar documents to “Jacobi-Eisenstein series and p -adic interpolation of symmetric squares of cusp forms”

Heegner cycles, modular forms and jacobi forms

Nils-Peter Skoruppa (1991)

Journal de théorie des nombres de Bordeaux

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We give a geometric interpretation of an arithmetic rule to generate explicit formulas for the Fourier coefficients of elliptic modular forms and their associated Jacobi forms. We discuss applications of these formulas and derive as an example a criterion similar to Tunnel's criterion for a number to be a congruent number.

Jacobi-Eisenstein series of degree two over Cayley numbers.

Minking Eie (2000)

Revista Matemática Iberoamericana

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We shall develop the general theory of Jacobi forms of degree two over Cayley numbers and then construct a family of Jacobi- Eisenstein series which forms the orthogonal complement of the vector space of Jacobi cusp forms of degree two over Cayley numbers. The construction is based on a group representation arising from the transformation formula of a set of theta series.

p -adic L -functions of Hilbert modular forms

Andrzej Dabrowski (1994)

Annales de l'institut Fourier

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We construct p -adic L -functions (in general case unbounded) attached to “motivic" primitive Hilbert cusp forms as a non-archimedean Mellin transform of the corresponding admissible measure. In order to prove the growth conditions of the appropriate complex-valued distributions we represent them as Rankin type representation and use Atkin–Lehner theory and explicit form of Fourier coefficients of Eisenstein series.

p -adic measures attached to Siegel modular forms

Siegfried Böcherer, Claus-Günther Schmidt (2000)

Annales de l'institut Fourier

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We study the critical values of the complex standard- L -function attached to a holomorphic Siegel modular form and of the twists of the L -function by Dirichlet characters. Our main object is for a fixed rational prime number p to interpolate p -adically the essentially algebraic critical L -values as the Dirichlet character varies thus providing a systematic control of denominators of critical values by generalized Kummer congruences. In order to organize this information we prove the existence...