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On Affine Minimal Translation Surfaces and Ramanujan Identities

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Abstract

In this paper, using the Weierstrass–Enneper formula and the hodographic coordinate system, we find the relationships between the Ramanujan identity and a generalized class of minimal translation surfaces, known as affine minimal translation surfaces. We find the Dirichlet series expansion of the affine Scherk surface. We also obtain some of the probability measures of affine Scherk surface with respect to its logarithmic distribution. Next, we classify the affine minimal translation surfaces in \({\mathbb {L}}^3\) and remark the analogous forms in \({\mathbb {L}}^3.\)

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Acknowledgements

I am very thankful to the anonymous referees for their valuable comments which helped a lot to improve the article. I am also thankful to Prof. Rukmini Dey for having valuable discussions.

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  1. International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru, 560089, India

    Mohamd Saleem Lone

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  1. Mohamd Saleem Lone
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Correspondence to Mohamd Saleem Lone.

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Lone, M.S. On Affine Minimal Translation Surfaces and Ramanujan Identities. Mediterr. J. Math. 18, 188 (2021). https://doi.org/10.1007/s00009-021-01849-8

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  • DOI: https://doi.org/10.1007/s00009-021-01849-8

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