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Efficient computation of multidimensional theta functions

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J. Frauendiener, C. Jaber, C. Klein

Exactly Solvable and Integrable Systems · Submitted 25 Jan 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim An algorithm is presented to approximately map the Riemann matrix to the Siegel fundamental domain.

how it is stated · asserted 1.00 read the record →

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arXiv ID1701.07486 (version 1)
Pith IDNNLXZJME, Pith's permanent record of this paper and its review
CitationC. Jaber, C. Klein, J. Frauendiener. "Efficient computation of multidimensional theta functions." arXiv:1701.07486 (2017). https://pith.science/paper/NNLXZJME
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,250 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.29 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.96 · compares with prior results 0.87 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

An important step in the efficient computation of multi-dimensional theta functions is the construction of appropriate symplectic transformations for a given Riemann matrix assuring a rapid convergence of the theta series. An algorithm is presented to approximately map the Riemann matrix to the Siegel fundamental domain. The shortest vector of the lattice generated by the Riemann matrix is identified exactly, and the algorithm ensures that its length is larger than $\sqrt{3}/2$. The approach is based on a previous algorithm by Deconinck et al. using the LLL algorithm for lattice reductions. Here, the LLL algorithm is replaced by exact Minkowski reductions for small genus and an exact identification of the shortest lattice vector for larger values of the genus.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 An important step in the efficient computation of multi-dimensional theta functions is the construction of appropriate symplectic transformations for a given Riemann matrix assuring a rapid convergence of the theta series. background 1.00 0.09 0.11 asserted 1.00
s1 An algorithm is presented to approximately map the Riemann matrix to the Siegel fundamental domain. contribution 0.78 0.91 0.22 asserted 1.00
s2 The shortest vector of the lattice generated by the Riemann matrix is identified exactly, and the algorithm ensures that its length is larger than $\sqrt{3}/2$. result 0.44 0.87 0.20 asserted 1.00
s3 The approach is based on a previous algorithm by Deconinck et al. using the LLL algorithm for lattice reductions. background 0.84 0.08 0.04 asserted 1.00
s4 Here, the LLL algorithm is replaced by exact Minkowski reductions for small genus and an exact identification of the shortest lattice vector for larger values of the genus. method 0.66 0.85 0.17 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 0.60.

What was examined, and what was not

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  • T body sentences
  • C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

An important step in the efficient computation of multi-dimensional theta functions is the construction of appropriate symplectic transformations for a given Riemann matrix assuring a rapid convergence of the theta series. An algorithm is presented to approximately map the Riemann matrix to the Siegel fundamental domain. The shortest vector of the lattice generated by the Riemann matrix is identified exactly, and the algorithm ensures that its length is larger than $\sqrt{3}/2$. The approach is based on a previous algorithm by Deconinck et al. using the LLL algorithm for lattice reductions. Here, the LLL algorithm is replaced by exact Minkowski reductions for small genus and an exact identification of the shortest lattice vector for larger values of the genus.

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