Skip to main content Accessibility help
×
×
Home

Vanishing sums in function fields

  • W. D. Brownawell (a1) and D. W. Masser (a2)

Extract

Let k be a field of zero characteristic, and let F be a function field over k of genus g. We normalize each valuation v on F so that its order group consists of all rational integers, and for elements u1, …, un of F, not all zero, we define the (projective) height as

The sum formula on F shows that this is really a height on the projective space .

Copyright

References

Hide All
[1]Cartan, H.. Sur les zéros de combinaisons linéaires de p fonctions holomorphes données. Mathematica Cluj 7 (1933), 529;
Collected Works, vol. 1 (ed. Remmert, R. and Serre, J.-P.) (Springer-Verlag, 1979), 421445.
[2]Hayman, W. K.. Waring's Problem für analytische Funktionen. Bayerische Akademie der Wissenschaften, Math.-Nat. Klasse no. 1 (1984).
[3]Mason, R. C.. Diophantine Equations over Function Fields. London Math. Soc. Lecture Notes, vol. 96 (Cambridge University Press, 1984).
[4]Mason, R. C.. Norm form equations. I. J. Number Theory 22 (1986), 190207 (see also similar titles II, III, IV, V).
[5]Muir, T. and Metzler, W. H.. A Treatise on the Theory of Determinants (Dover, 1960).
[6]Silverman, J. H.. The S-unit equation over function fields. Math. Proc. Cambridge Philos. Soc. 95 (1984), 34.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed