On the product of heights of algebraic numbers summing to real numbers
Some infinite products with interesting continued fraction expansions
We display several infinite products with interesting continued fraction expansions. Specifically, for various small values of necessarily excluding since that case cannot occur, we display infinite products in the field of formal power series whose truncations yield their every -th convergent.
Heights of roots of polynomials with odd coefficients
Let be a zero of a polynomial of degree with odd coefficients, with not a root of unity. We show that the height of satisfies More generally, we obtain bounds when the coefficients are all congruent to modulo for some .
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