Timeline for Bounds on coefficients of factors of a multivariate polynomial
Current License: CC BY-SA 3.0
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| Dec 14, 2013 at 19:19 | comment | added | Joe Silverman | Right. And now that you mention it, Lang includes this in his book because "Michel Waldschmidt recommended their inclusion" (page 59). So Prop 2.12 on page 61 says that if $f,g\in\mathbb{C}[X_1,\ldots,X_n]$ and if $fg$ has total degree at most $d$, then $|f|_\infty|g|_\infty\le e^{nd}|fg|_\infty$. The proof, as you indicate, uses Mahler measure. Lang refers to Gelfond's book, as well as the article by Mahler that you quote. | |
| Dec 14, 2013 at 18:56 | history | answered | Douglas Lind | CC BY-SA 3.0 |