# Asymptotic expansion of the difference of two Mahler measures

@article{Condon2011AsymptoticEO, title={Asymptotic expansion of the difference of two Mahler measures}, author={John Donald Condon}, journal={arXiv: Number Theory}, year={2011} }

We show that for almost every polynomial P(x,y) with complex coefficients, the difference of the logarithmic Mahler measures of P(x,y) and P(x,x^n) can be expanded in a type of formal series similar to an asymptotic power series expansion in powers of 1/n. This generalizes a result of Boyd. We also show that such an expansion is unique and provide a formula for its coefficients. When P has algebraic coefficients, the coefficients in the expansion are linear combinations of polylogarithms of… CONTINUE READING

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