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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Modular forms for $ G\sb{0}(N)$ and Dirichlet series


Author: Michael J. Razar
Journal: Trans. Amer. Math. Soc. 231 (1977), 489-495
MSC: Primary 10D15
MathSciNet review: 0444576
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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 Über 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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0444576-9
PII: S 0002-9947(1977)0444576-9
Keywords: Modular form, Dirichlet series
Article copyright: © Copyright 1977 American Mathematical Society