Modular forms for $G_{0}(N)$ and Dirichlet series
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- by Michael J. Razar PDF
- Trans. Amer. Math. Soc. 231 (1977), 489-495 Request permission
Abstract:
A criterion is given for a function to be a modular form for ${\Gamma _0}(N)$. It is similar to the criterion given by Weil in his 1967 Math. Ann. paper รber die Bestimmung Dirichletscher Reihen durch Funktional-gleichungen in that it involves checking that certain twists of the associated Dirichlet series satisfy functional equations. It differs in the number and type of such equations which need to be satisfied.References
- A. O. L. Atkin and J. Lehner, Hecke operators on $\Gamma _{0}(m)$, Math. Ann. 185 (1970), 134โ160. MR 268123, DOI 10.1007/BF01359701
- Andrew P. Ogg, On the eigenvalues of Hecke operators, Math. Ann. 179 (1969), 101โ108. MR 269597, DOI 10.1007/BF01350121
- Andrew Ogg, Modular forms and Dirichlet series, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0256993
- Michael J. Razar, On the transformation of $\textrm {log}\eta$, Illinois J. Math. 21 (1977), no.ย 2, 305โ314. MR 437464
- Andrรฉ Weil, รber die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann. 168 (1967), 149โ156 (German). MR 207658, DOI 10.1007/BF01361551
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 231 (1977), 489-495
- MSC: Primary 10D15
- DOI: https://doi.org/10.1090/S0002-9947-1977-0444576-9
- MathSciNet review: 0444576