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INTEGERS REPRESENTED BY $x^{4}-y^{4}$ REVISITED

Part of: Diophantine equations Discontinuous groups and automorphic forms Arithmetic algebraic geometry

Published online by Cambridge University Press:  20 May 2020

MICHAEL A. BENNETT Open the ORCID record for MICHAEL A. BENNETT [Opens in a new window]
MICHAEL A. BENNETT*
Affiliation:
Department of Mathematics,University of British Columbia, Vancouver, BC, Canada V6T 1Z2 email bennett@math.ubc.ca
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Abstract

We sharpen earlier work of Dabrowski on near-perfect power values of the quartic form $x^{4}-y^{4}$, through appeal to Frey curves of various signatures and related techniques.

Keywords

Diophantine equationsFrey curvesmodularity

MSC classification

Primary: 11D41: Higher degree equations; Fermat's equation
Secondary: 11F33: Congruences for modular and $p$-adic modular forms 11F80: Galois representations 11G05: Elliptic curves over global fields
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 1 , February 2021 , pp. 38 - 49
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

The author was partially supported by a grant from NSERC.

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