On the spatial distribution of solutions of decomposable form equations
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- by G. Everest, I. Gaál, K. Györy and C. Röttger PDF
- Math. Comp. 71 (2002), 633-648 Request permission
Abstract:
We study the distribution in space of the integral solutions to an integral decomposable form equation, by considering the images of these solutions under central projection onto a unit ball. If we think of the solutions as stars in the night sky, we ask what constellations are visible from the earth (the unit ball). Answers are given for a large class of examples which are then illustrated using the software packages KANT and Maple. These pictures highlight the accuracy of our predictions and arouse interest in cases not covered by our results. Within the range of applicability of our results lie solutions to norm form equations and units in abelian group rings. Thus our theory has a lot to say about where these interesting objects can be found and what they look like.References
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Additional Information
- G. Everest
- Affiliation: School of Mathematics, University of East Anglia, Norwich, Norfolk NR4 7TJ, United Kingdom
- Email: g.everest@uea.ac.uk
- I. Gaál
- Affiliation: Institute of Mathematics and Informatics, Lajos Kossuth University, H-4010 Debrecen, Pf 12, Hungary
- Email: igaal@math.klte.hu
- K. Györy
- Affiliation: Institute of Mathematics and Informatics, Lajos Kossuth University, H-4010 Debrecen, Pf 12, Hungary
- Email: gyory@math.klte.hu
- C. Röttger
- Affiliation: School of Mathematics, University of East Anglia, Norwich, Norfolk NR4 7TJ, United Kingdom
- Email: C.Rottger@uea.ac.uk
- Received by editor(s): July 13, 1999
- Received by editor(s) in revised form: June 6, 2000
- Published electronically: August 3, 2001
- Additional Notes: Röttger’s research was supported by a PhD grant from the UEA. Györy thanks the LMS for a scheme 2 grant at an early stage of this research. Györy and Gaál were supported by the Hungarian Academy of Sciences and by grants 16975, 25157 and 29330 from the Hungarian National Foundation for Scientific Research.
- © Copyright 2001 American Mathematical Society
- Journal: Math. Comp. 71 (2002), 633-648
- MSC (2000): Primary 11D57, 11Y50
- DOI: https://doi.org/10.1090/S0025-5718-01-01353-9
- MathSciNet review: 1885618