Pith. Sign in

RECORD

On the moments of Hecke series at central points II

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Aleksandar Ivic, Matti Jutila

Number Theory · Submitted 13 May 2003

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

The authors' main claim We prove, in standard notation from spectral theory, the asymptotic formula ($B>0$) $$ \sum_{\kappa_j\le T}\alpha_j H_j(1/2) = ({T\over\pi})^2 - BT\log T + O(T(\log T)^{1/2}), $$ by using an approximate functional equation for $H_j(1/2)$ and the Bruggeman--Kuznetsov trace formula.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv IDmath/0305178 (version 3)
Pith IDUU2RGW54, Pith's permanent record of this paper and its review
CitationAleksandar Ivic, Matti Jutila. "On the moments of Hecke series at central points II." arXiv:math/0305178 (2003). https://pith.science/paper/UU2RGW54
Claim paper

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.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,438 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.54 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.97 · compares with prior results 0.14 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We prove, in standard notation from spectral theory, the asymptotic formula ($B>0$) $$ \sum_{\kappa_j\le T}\alpha_j H_j(1/2) = ({T\over\pi})^2 - BT\log T + O(T(\log T)^{1/2}), $$ by using an approximate functional equation for $H_j(1/2)$ and the Bruggeman--Kuznetsov trace formula. We indicate how the error term may be improved to $O(T(\log T)^\epsilon)$.

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 We prove, in standard notation from spectral theory, the asymptotic formula ($B>0$) $$ \sum_{\kappa_j\le T}\alpha_j H_j(1/2) = ({T\over\pi})^2 - BT\log T + O(T(\log T)^{1/2}), $$ by using an approximate functional equation for $H_j(1/2)$ and the Bruggeman--Kuznetsov trace formula. result 0.91 0.96 0.95 asserted 1.00
s1 We indicate how the error term may be improved to $O(T(\log T)^\epsilon)$. future work 0.74 0.76 0.04 hedged possibility 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

sources read
  • arXiv listing abstract v3
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • 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

We prove, in standard notation from spectral theory, the asymptotic formula ($B>0$) $$ \sum_{\kappa_j\le T}\alpha_j H_j(1/2) = ({T\over\pi})^2 - BT\log T + O(T(\log T)^{1/2}), $$ by using an approximate functional equation for $H_j(1/2)$ and the Bruggeman--Kuznetsov trace formula. We indicate how the error term may be improved to $O(T(\log T)^\epsilon)$.

Human review

How Pith checks papers → · Full audit of this paper →

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.