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}
}
  • John Donald Condon
  • Published 2011
  • Mathematics
  • arXiv: Number Theory
  • 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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