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Nested ansatz method for Baker-Akhiezer functions

A. Mironov2,3,4,*, A. Morozov1,3,4,†, and A. Popolitov1,3,4,‡

  • *Contact author: mironov@lpi.ru, mironov@itep.ru
  • †Contact author: morozov@itep.ru
  • ‡Contact author: popolit@gmail.com
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Phys. Rev. D 113, 126019 – Published 16 June, 2026

DOI: https://doi.org/10.1103/962c-lnng

Abstract

We explain that the logic behind the derivation of the Noumi-Shiraishi function can be applied directly to the Baker-Akhiezer function (BAF). This amounts to changing an ansatz for BAF to a nested one, where the BAF of N+1 variables is recursively expressed as a sum over BAFs of N variables. This may be seen as a generalization of symmetrization trick from [A. Mironov, A. Morozov, and A. Popolitov, arXiv:2601.10500] but for the generally nonsymmetric BAF. We demonstrate that, for usual nontwisted (a=1) BAFs, this method correctly reproduces the Noumi-Shiraishi formula directly from linear equations, resolving the ambiguity related to nonsimple roots. For the first nontrivial twisted case (N=3, a=2) this method also fixes this ambiguity, moreover, answers for the first few layers of coefficients are in the form of direct quantization of the above article.

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Phys. Rev. D 113, 126019– Published 16 June, 2026
  • Received 17 March 2026
  • Accepted 21 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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