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A fresh approach to classical Eisenstein series and the newer Hilbert-Eisenstein series

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Paul L. Butzer, Tibor K. Pogány

Classical Analysis and ODEs · Submitted 12 Apr 2016

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

The authors' main claim The latter turn out to be the product of the hyperbolic sinh--function with an explicit closed form linear combination of digamma functions.

how it is stated · asserted 0.99 read the record →

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arXiv ID1604.03245 (version 1)
Pith IDJQSWTJP4, Pith's permanent record of this paper and its review
CitationPaul L. Butzer, Tibor K. Pog\'any. "A fresh approach to classical Eisenstein series and the newer Hilbert-Eisenstein series." arXiv:1604.03245 (2016). https://pith.science/paper/JQSWTJP4
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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, 3,698 input tokens.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.39 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

This paper is concerned with new results for the circular Eisenstein series $\varepsilon_r(z)$ as well as with a novel approach to Hilbert-Eisenstein series $\mathfrak h_r(z)$, introduced by Michael Hauss in 1995. The latter turn out to be the product of the hyperbolic sinh--function with an explicit closed form linear combination of digamma functions. The results, which include differentiability properties and integral representations, are established by independent and different argumentations. Highlights are new results on the Butzer--Flocke--Hauss Omega function, one basis for the study of Hilbert-Eisenstein series, which have been the subject of several recent papers.

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 This paper is concerned with new results for the circular Eisenstein series $\varepsilon_r(z)$ as well as with a novel approach to Hilbert-Eisenstein series $\mathfrak h_r(z)$, introduced by Michael Hauss in 1995. contribution 0.94 0.52 0.10 asserted 0.98
s1 The latter turn out to be the product of the hyperbolic sinh--function with an explicit closed form linear combination of digamma functions. result 1.00 0.76 0.29 asserted 0.99
s2 The results, which include differentiability properties and integral representations, are established by independent and different argumentations. method 0.95 0.84 0.10 asserted 1.00
s3 Highlights are new results on the Butzer--Flocke--Hauss Omega function, one basis for the study of Hilbert-Eisenstein series, which have been the subject of several recent papers. contribution 0.80 0.73 0.13 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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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

This paper is concerned with new results for the circular Eisenstein series $\varepsilon_r(z)$ as well as with a novel approach to Hilbert-Eisenstein series $\mathfrak h_r(z)$, introduced by Michael Hauss in 1995. The latter turn out to be the product of the hyperbolic sinh--function with an explicit closed form linear combination of digamma functions. The results, which include differentiability properties and integral representations, are established by independent and different argumentations. Highlights are new results on the Butzer--Flocke--Hauss Omega function, one basis for the study of Hilbert-Eisenstein series, which have been the subject of several recent papers.

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