Short walk adventures

Straub, Armin; Zudilin, Wadim

doi:10.1007/978-3-030-36568-4_27

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Short walk adventures

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Straub, Armin
Max Planck Institute for Mathematics, Max Planck Society;

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Zudilin, Wadim
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/978-3-030-36568-4_27
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https://doi.org/10.1007/978-3-030-36568-4_28
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arXiv:1801.06002.pdf
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Citation

Straub, A., & Zudilin, W. (2020). Short walk adventures. In D. H. Bailey (Ed.), From analysis to visualization (pp. 423-439). Cham: Springer.

Cite as: https://hdl.handle.net/21.11116/0000-0006-8EB4-F

Abstract

We review recent development of short uniform random walks, with a focus on
its connection to (zeta) Mahler measures and modular parametrisation of the
density functions. Furthermore, we extend available "probabilistic" techniques
to cover a variation of random walks and reduce some three-variable Mahler
measures, which are conjectured to evaluate in terms of $L$-values of modular
forms, to hypergeometric form.