Second order modular forms
G. Chinta, N. Diamantis (2002)
Acta Arithmetica
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G. Chinta, N. Diamantis (2002)
Acta Arithmetica
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Shinji Fukuhara (2012)
Acta Arithmetica
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Stephen S. Kudla (1979)
Inventiones mathematicae
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Karen Taylor (2012)
Acta Arithmetica
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D. Zagier, W. Kohnen (1981)
Inventiones mathematicae
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Karl Mahlburg, Ken Ono (2004)
Acta Arithmetica
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Svetlana Katok (1985)
Inventiones mathematicae
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Benedict H. Gross, Kevin Keating (1993)
Inventiones mathematicae
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Ernst-Ulrich Gekeler (1988)
Inventiones mathematicae
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Alexandru Buium, Arnab Saha (2011)
Banach Center Publications
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We prove that some of the basic differential functions appearing in the (unramified) theory of arithmetic differential equations, especially some of the basic differential modular forms in that theory, arise from a "ramified situation". This property can be viewed as a special kind of overconvergence property. One can also go in the opposite direction by using differential functions that arise in a ramified situation to construct "new" (unramified) differential functions.
Don Zagier (1975)
Inventiones mathematicae
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Larry J. Gerstein (1972)
Inventiones mathematicae
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