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Computing isogeny covariant differential modular forms

Author: Chris Hurlburt
Journal: Math. Comp. 74 (2005), 905-926
MSC (2000): Primary 11F11; Secondary 12H05
Published electronically: October 29, 2004
MathSciNet review: 2114654
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Abstract | References | Similar Articles | Additional Information

Abstract: We present the computation modulo $p^2$ and explicit formulas for the unique isogeny covariant differential modular form of order one and weight $\chi _{-p-1,-p}$ called $f_{\operatorname{jet}}$, an isogeny covariant differential modular form of order two and weight $\chi _{-p^2-p,-1,-1}$ denoted by $f_{\operatorname{jet}}h_{\operatorname{jet}}$, and an isogeny covariant differential modular form $h_{\operatorname{jet}}$ of order two and weight $\chi _{1-p^2,0,-1}$.

References [Enhancements On Off] (What's this?)

  • 1. M. Barcau and A. Buium, Siegel Differential Modular Forms, Int. Math. Res. Not. (2002), no. 28, 1457-1503. MR 1908022 (2003g:11044)
  • 2. A. Buium, Geometry of Fermat Adeles, Preprint, 1999.
  • 3. -, Differential Modular Forms, J. Reine Angew. Math. (2000), no. 520, 95-167.MR 1748272 (2002d:11042)
  • 4. -, Arithmetic Differential Invariants, In preparation, 2003.
  • 5. C. Hurlburt, Isogeny Covariant Differential Modular Forms modulo $p$, Compositio Mathematica 128 (2001), no. 1, 17-34. MR 1847663 (2002i:11053)
  • 6. J. Silverman, The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics, vol. 106, Springer Verlag, 1986. MR 0817210 (87g:11070)

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Additional Information

Chris Hurlburt
Affiliation: Department of Mathematics, Northern Illinois University, DeKalb, Illinois 60115

Received by editor(s): January 14, 2004
Received by editor(s) in revised form: April 16, 2004
Published electronically: October 29, 2004
Additional Notes: This research was supported in part by NSA grant MDA904-03-1-0031
Article copyright: © Copyright 2004 American Mathematical Society

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