Publications

You can also find my articles on my Google Scholar profile.

Journal Articles

Computation and properties of the Epstein zeta function with applications to quantum systems

Published in IMA Journal of Numerical Analysis, 2026

This paper establishes the Epstein zeta function as a powerful tool in numerical analysis by rigorously investigating its analytical properties and enabling its efficient computation.

Recommended citation: Buchheit, A. A., Busse, J. K., & Gutendorf, R. (2026). "Computation and properties of the Epstein zeta function with applications to quantum systems." IMA Journal of Numerical Analysis, drag057. DOI: 10.1093/imanum/drag057
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Zeta Expansion for Long-Range Interactions under Periodic Boundary Conditions with Applications to Micromagnetics

Published in Journal of Computational Physics, 2026

This paper addresses the efficient computation of power-law-based interaction potentials of homogeneous n-dimensional bodies with an infinite d-dimensional array of copies, including their higher-order derivatives.

Recommended citation: Buchheit, A. A., Busse, J. K., Keßler, T., & Rybakov, F. N. (2026). "Zeta Expansion for Long-Range Interactions under Periodic Boundary Conditions with Applications to Micromagnetics." Journal of Computational Physics, 114885. DOI: 10.1016/j.jcp.2026.114885
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Exact lattice summations for Lennard-Jones potentials coupled to a three-body Axilrod-Teller-Muto term applied to cuboidal phase transitions

Published in Journal of Chemical Physics, 2025

This paper provides a rigorous analysis of Bain-type cuboidal lattice transformations, incorporating a general (n,m) Lennard-Jones two-body potential and a long-range repulsive Axilrod-Teller-Muto (ATM) three-body potential.

Recommended citation: Robles-Navarro, A., Cooper, S., Buchheit, A. A., Busse, J. K., Burrows, A., Smits, O., & Schwerdtfeger, P. (2025). "Exact lattice summations for Lennard-Jones potentials coupled to a three-body Axilrod-Teller-Muto term applied to cuboidal phase transitions." J. Chem. Phys. 163, 094104. DOI: 10.1063/5.0276677
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Preprints

Epstein zeta method for many-body lattice sums

Published in arXiv, 2025

This paper presents an efficiently computable representation of many-body lattice sums in terms of singular integrals over products of Epstein zeta functions.

Recommended citation: Buchheit, A. A., & Busse, J. K. (2025). "Epstein zeta method for many-body lattice sums." arXiv preprint arXiv:2504.11989.
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Software

EpsteinLib: Fast and Efficient Computation of the Epstein Zeta Function

Published in GitHub, 2024

EpsteinLib is a C library and Python package for fast and efficient computation of the Epstein zeta function for arbitrary multidimensional lattices.

Recommended citation: Buchheit, A. A., Busse, J., Gutendorf, R., & Schmitz, J. (2024). EpsteinLib: Fast and Efficient Computation of the Epstein Zeta Function. GitHub. https://github.com/epsteinlib/epsteinlib
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Jonathan K. Busse