The coefficients of $f$ are elements of $F(S)$. Thus each coefficient of $f$ looks like a ratio of two polynomials over $F$ evaluated on some members...
I have have shown that $k$ is a common multiple of the $\exp(H_i)$. Since $m$ is the least common multiple of the $\exp(H_i)$, then $k$ is a multiple...
I obtained a master's degree in mechanical engineering in May 2014.
Then I went on to join a master's programme in mathematics and obtained a master's degree in July 2016. I am currently a first year PhD student in mathematics. I love fountain pens and am a die hard fan of the Prince of Persia 2008 video game.