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Posts
What does the Epstein zeta function actually do?
Published:
When I first started studying mathematics at university, I was obsessed with popular math problems, such as the Riemann Hypothesis. The conjecture states that all zeros of the Riemann zeta function other than \(-2, -4, -6\), … lie on the critical line \(\operatorname{Re}(\nu) = 1/2\). If proven, this would earn you a million dollars 💸
Reflections on APS Summit 2025: Quantum Breakthroughs and Epstein Zeta Function
Published:
Just got back from the biggest physics conference of the world, the #APSSummit25 hosted in Los Angeles 😁.
publications
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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Computation and properties of the Epstein zeta function with high-performance implementation in EpsteinLib
Published in arXiv, 2024
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., & Gutendorf, R. (2024). "Computation and properties of the Epstein zeta function with high-performance implementation in EpsteinLib." arXiv preprint arXiv:2412.16317.
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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 arXiv, 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." arXiv preprint arXiv:2504.07338.
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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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talks
Computation and properties of the Epstein zeta function: Application and numerical challenges
Published:
Session: Friday, August 23 Time: 09:30 - 09:50
Computation and properties of the Epstein zeta function: EpsteinLib for precision many-body Physics
Published:
Session: MAR-T47 Room: 262B Time: Thursday, 4:36 PM
teaching
WS 2019/2020: Introductory Course to University Mathematics
Undergraduate course, University of Duisburg-Essen, 2019
Introductory course to prepare students for University Mathematics at University of Duisburg-Essen for the winter semester 2019/2020.
WS 2020/2021: Introductory Course to University Mathematics
Undergraduate course, University of Duisburg-Essen, 2020
Introductory course to prepare students for University Mathematics at University of Duisburg-Essen for the winter semester 2020/2021.
WS 2021/2022: Analysis II Intensive Course
Undergraduate course, Heinrich Heine University Düsseldorf, 2021
Intensive course to prepare for the Analysis II re-examination for the winter semester 2021/2022 at Heinrich Heine University Düsseldorf.
SS 2022: Analysis II Intensive Course
Undergraduate course, Heinrich Heine University Düsseldorf, 2022
Intensive course to prepare for the Analysis II re-examination for the summer semester 2022 at Heinrich Heine University Düsseldorf.