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31.
We characterize the function spanned by theta series. As an application we derive a simple proof of the modular identity of the theta series.
32.
A special case of a fundamental theorem of Schneider asserts that if \(j(\tau )\) is algebraic (where j is the classical modular invariant), then any zero z not in \(\mathbf{Q}.L_\tau := \mathbf{Q}\oplus \mathbf{Q}\tau \) of the Weierstrass function \(\wp (\tau ,\cdot )\) attached to the lattice \(L_\tau =\mathbf{Z}\oplus \mathbf{Z}\tau \) is transcendental. In this note we generalize this result to holomorphic Jacobi forms of weight k and index \(m\in \mathbf{N}\) with algebraic Fourier coefficients. 相似文献
33.
Vignéras constructs non-holomorphic theta functions according to indefinite quadratic forms with arbitrary signature. We use
Vignéras’ theta functions to create examples of non-holomorphic Jacobi forms associated to indefinite theta series by two
different methods. 相似文献
34.
Let be a Siegel modular form of weight ?, and let be an Eichler embedding, where denotes the Siegel upper half space of degree n. We use the notion of mixed Siegel modular forms to construct the linear map of the spaces of Siegel cusp forms for the congruence subgroup and express the Fourier coefficients of the image of an element under in terms of special values of a certain Dirichlet series. We also discuss connections between mixed Siegel cusp forms and holomorphic forms on a family of abelian varieties. 相似文献
35.
We incorporate the non-critical values of L-functions of cusp forms into a cohomological set-up analogous to the one of Eichler, Manin and Shimura. We use the 1-cocycles
we associate in this way to non-critical values to prove an expression for such values which is similar in structure to Manin’s
formula for the critical value of the L-function of a weight 2 cusp form.
YoungJu Choie is partially supported by KOSEF R01-2003-00011596-0 and by ITRC Research Fund.
N. Diamantis is partially supported by EPSRC grant EP/D032350/1. 相似文献
36.
In this paper, we study congruence properties of coefficient of Jacobi forms. The result for elliptic modular form case was
studied by Sturm (Lecture Notes in Mathematics, Springer, Berlin Heidelberg New York 1987). 相似文献
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40.
The Rankin–Cohen product of two modular forms is known to be a modular form. The same formula can be used to define the Rankin–Cohen
product of two holomorphic functions f and g on the upper half-plane. Assuming that this product is a modular form, we prove that both f and g are modular forms if one of them is. We interpret this result in terms of solutions of linear ordinary differential equations. 相似文献