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The Characteristic Exponents of a Pair of Power Series

Published online by Cambridge University Press:  24 October 2008

S. Lilley
S. Lilley
Affiliation:
St John's CollegeCambridge
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Abstract

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Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 37 , Issue 1 , January 1941 , pp. 105 - 108
Copyright
Copyright © Cambridge Philosophical Society 1941

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References

* See, e.g. Enriques-Chisini, , Teoria geometrica delle equazioni, 2 (Bologna, 1918), 327–92, especially pp. 374–7.Google Scholar

† In Coolidge, , A treatise on algebraic plane curves (Oxford, 1931), 221–2,Google Scholar a special case of the problem dealt with below is considered.

‡ For example, a curve branch in three dimensions in its simplest form is given by equations of the type x = tρ, y = t σP, z = t τQ (P, Q being power series in t, not vanishing at t = 0). But any plane projection of this branch (except from the points at infinity on the axes of y or z) has the general form (2) above.