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Plane curves and p-adic roots of unity

Published online by Cambridge University Press:  17 April 2009

José Felipe Voloch
José Felipe Voloch
Affiliation:
Department of MathematicsUniversity of TexasAustin TX 78712United States of America e-mail: [email protected]
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We prove the following result: Let f(x, y) be a polynomial of degree d in two variables whose coefficents are integers in an unramified extension of Qp. Assume that the reduction of f modulo p is irreducible of degree d and not a binomial. Assume also that p > d2 + 2. Then the number of solutions of the inequality |f(ζ1, ζ2)| < p−1, with ζ1, ζ2 roots of unity in Q̄p or zero, is at most pd2.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 60 , Issue 3 , December 1999 , pp. 479 - 482
Copyright
Copyright © Australian Mathematical Society 1999

References

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