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Estimates of automorphic forms over quaternion algebras

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Anilatmaja Aryasomayajula, Baskar Balasubramanyam

Number Theory · Submitted 21 Aug 2017

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

The authors' main claim Using which, we prove an average version of the holomorphic QUE conjecture.

how it is stated · asserted 0.99 read the record →

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arXiv ID1708.06174 (version 1)
Pith IDKHSFJ2A2, Pith's permanent record of this paper and its review
CitationAnilatmaja Aryasomayajula, Baskar Balasubramanyam. "Estimates of automorphic forms over quaternion algebras." arXiv:1708.06174 (2017). https://pith.science/paper/KHSFJ2A2
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The compiled record

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, 3,486 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.79 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

In this article, using methods from geometric analysis and theory of heat kernels, we derive qualitative estimates of automorphic cusp forms defined over quaternion algebras. Using which, we prove an average version of the holomorphic QUE conjecture. We then derive quantitative estimates of classical Hilbert modular cusp forms. This is a generalization of the results from [3] and [9] to higher dimensions.

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 In this article, using methods from geometric analysis and theory of heat kernels, we derive qualitative estimates of automorphic cusp forms defined over quaternion algebras. contribution 0.93 0.96 0.26 asserted 1.00
s1 Using which, we prove an average version of the holomorphic QUE conjecture. result 0.95 0.92 0.39 asserted 0.99
s2 We then derive quantitative estimates of classical Hilbert modular cusp forms. result 0.54 0.96 0.20 asserted 1.00
s3 This is a generalization of the results from [3] and [9] to higher dimensions. contribution 0.43 0.59 0.07 asserted 1.00

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

What was examined, and what was not

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  • arXiv listing abstract v1
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  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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

In this article, using methods from geometric analysis and theory of heat kernels, we derive qualitative estimates of automorphic cusp forms defined over quaternion algebras. Using which, we prove an average version of the holomorphic QUE conjecture. We then derive quantitative estimates of classical Hilbert modular cusp forms. This is a generalization of the results from [3] and [9] to higher dimensions.

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