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A new bound for the error term in the approximate functional equation for the derivatives of the Hardy's Z-function

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Philippe Blanc

Number Theory · Submitted 3 Sep 2018

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

The authors' main claim We obtain a new bound of this error term which is much better for high order derivatives.

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arXiv ID1809.00735 (version 1)
Pith IDPG6SOIRX, Pith's permanent record of this paper and its review
CitationPhilippe Blanc. "A new bound for the error term in the approximate functional equation for the derivatives of the Hardy's Z-function." arXiv:1809.00735 (2018). https://pith.science/paper/PG6SOIRX
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,226 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.36 · compares with prior results 0.93 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Lavrik and the author gave uniform bounds of the error term in the approximate functional equation for the derivatives of the Hardy's Z-function. We obtain a new bound of this error term which is much better for high order derivatives.

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 Lavrik and the author gave uniform bounds of the error term in the approximate functional equation for the derivatives of the Hardy's Z-function. background 1.00 0.65 0.06 asserted 1.00
s1 We obtain a new bound of this error term which is much better for high order derivatives. contribution 0.50 0.96 0.94 asserted 1.00

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

Lavrik and the author gave uniform bounds of the error term in the approximate functional equation for the derivatives of the Hardy's Z-function. We obtain a new bound of this error term which is much better for high order derivatives.

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