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Level Lowering Modulo Prime Powers and Twisted Fermat Equations

Published online by Cambridge University Press:  20 November 2018

Sander R. Dahmen  and
Soroosh Yazdani
Sander R. Dahmen
Affiliation:
Department of Mathematics, The University of British Columbia, Vancouver, BC, V6T 1Z2 email: dahmen@math.ubc.ca
Soroosh Yazdani
Affiliation:
Department of Mathematics and Statistics, McMaster University, West Hamilton, ON, L8S 4K1 email: syazdani@math.mcmaster.ca
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Abstract

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We discuss a clean level lowering theorem modulo prime powers for weight 2 cusp forms. Furthermore, we illustrate how this can be used to completely solve certain twisted Fermat equations $a{{x}^{n}}\,+\,b{{y}^{n\,}}\,+\,c{{z}^{n}}\,=\,0$.

Keywords

11D4111F3311F1111F8011G05modular formslevel loweringDiophantine equations
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 64 , Issue 2 , 16 April 2012 , pp. 282 - 300
Copyright
Copyright © Canadian Mathematical Society 2012

References

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