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Record W1511232797 · doi:10.1017/cbo9780511756375.006

Gross–Zagier Revisited

2004· book-chapter· en· W1511232797 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

Venuenot available
Typebook-chapter
Languageen
FieldMathematics
TopicAlgebraic Geometry and Number Theory
Canadian institutionsMcGill University
Fundersnot available
KeywordsMathematics

Abstract

fetched live from OpenAlex

The aim of this paper is to rework the material in Chapter III of Gross and Zagier's "Heegner points and derivatives of L-series" —see [GZ] in the list of references—based on more systematic deformation-theoretic methods, so as to treat all imaginary quadratic fields, all residue characteristics, and all j-invariants on an equal footing. This leads to more conceptual arguments in several places and interpretations for some quantities which appear to otherwise arise out of thin air in [GZ, Ch. III]. For example, the sum in [GZ, Ch. III, Lemma 8.2] arises for us in (9−6), where it is given a deformation-theoretic meaning. Provided the analytic results in [GZ] are proven for even discriminants, the main results in [GZ] would be valid without parity restriction on the discriminant of the imaginary quadratic field. Our order of development of the basic results follows [GZ, Ch. III], but the methods of proof are usually quite different, making much less use of the "numerology" of modular curves.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Insufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Other · Consensus signal: Other
Teacher disagreement score0.183
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0010.000
Insufficient payload (model declined to judge)0.0660.004

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.037
GPT teacher head0.277
Teacher spread0.239 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Quick stats

Citations45
Published2004
Admission routes1
Has abstractyes

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Same topicAlgebraic Geometry and Number TheoryFrench-language works237,207