The number of solutions of norm form equations

Author:
Wolfgang M. Schmidt

Journal:
Trans. Amer. Math. Soc. **317** (1990), 197-227

MSC:
Primary 11D57; Secondary 11J25

DOI:
https://doi.org/10.1090/S0002-9947-1990-0961596-2

MathSciNet review:
961596

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Abstract: A norm form is a form with rational coefficients which factors into linear forms over but is irreducible or a power of an irreducible form over . It is known that a nondegenerate norm form equation has only finitely many solutions . We derive explicit bounds for the number of solutions. When has coefficients in , these bounds depend only on , and the degree of , but are independent of the size of the coefficients of .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1990-0961596-2

Article copyright:
© Copyright 1990
American Mathematical Society