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On the regular part of the Bloch Green’s function for the Laplacian: analytical formula and critical points

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This paper is concerned with the regular part of the Bloch Green’s function in a Wigner–Seitz lattice cell. We first give a new fast converging series expression. Then we derive explicit expression using some Dedekind eta functions when the Bloch vector \(\mathbf {k}\) are some rational numbers. Finally we study its critical points.

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Acknowledgements

S. Luo is grateful to Professor W.M. Zou (Tsinghua University) for his constant support and encouragement and would like to say special thanks to Professor H.J. Zhao (Wuhan University). The research of S. Luo is partially supported by double thousands plan of Jiangxi (jxsq2019101048) and NSFC (No. 12001253).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Jiangxi Normal University, Nanchang, 330022, People’s Republic of China

    Senping Luo

  2. Department of Mathematics, Washington and Lee University, Lexington, VA, 24450, USA

    Chong Wang

  3. Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada

    Juncheng Wei

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  1. Senping Luo
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  2. Chong Wang
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  3. Juncheng Wei
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Correspondence to Senping Luo.

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Luo, S., Wang, C. & Wei, J. On the regular part of the Bloch Green’s function for the Laplacian: analytical formula and critical points. Anal.Math.Phys. 11, 94 (2021). https://doi.org/10.1007/s13324-021-00528-x

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  • DOI: https://doi.org/10.1007/s13324-021-00528-x

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