mahler measure

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2025-08-29 · 1 min read

it isn't even a week into university and i already have a math equation to understand. i have a math class with prof. arunabha biswas and i checked out his work on the zeta mahler measure. now he is working on the closed formula for the measure. i really want to work with him on that publication, but he told me that the percentage of solving it is really really low. i really want to atleast understand the measure atleast though. so then we begin. the formula to understand is below.

M(p)=aαi1αi=ai=1nmax(1,αi)M(p) = |a| \prod_{|\alpha_i| \geq 1} |\alpha_i| = |a| \prod_{i=1}^n \max(1, |\alpha_i|)

where p(z)p(z) factorizes over the complex numbers C\mathbb{C} as:

p(z)=a(zα1)(zα2)...(zαn)p(z) = a(z - \alpha_1)(z - \alpha_2)...(z - \alpha_n)

the place to start apparently is complex analysis. so, time for some revision i guess. i will start with some youtube lectures. i need to buy notebooks for this. 3 notebooks it is, for my chemistry, math and this stuff. i really hope this leads somewhere.

ask.