A note on automorphic forms of weight one and weight three
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- by Peter F. Stiller PDF
- Trans. Amer. Math. Soc. 291 (1985), 503-518 Request permission
Abstract:
In this paper the author develops an interesting relationship between classical automorphic forms of weights one and three, and the solutions of certain second order differential equations related to elliptic (modular) surfaces. In particular for a cusp form of weight three, it is shown that the special values of the associated Dirichlet series can be determined from the periods of an inhomogeneous differential equation, or what is the same thing, the monodromy of an associated third order differential equation. Explicit examples are provided for principal congruence subgroups $\Gamma (N)$ with $N \equiv 0 \operatorname {mod} 4$.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 291 (1985), 503-518
- MSC: Primary 11F12; Secondary 14D05
- DOI: https://doi.org/10.1090/S0002-9947-1985-0800250-2
- MathSciNet review: 800250