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Record W4403515383 · doi:10.4171/cmh/577

Katz type $p$-adic $L$-functions for primes $p$ non-split in the $\mathrm{CM}$ field

2024· article· en· W4403515383 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

VenueCommentarii Mathematici Helvetici · 2024
Typearticle
Languageen
FieldMathematics
TopicAdvanced Algebra and Geometry
Canadian institutionsConcordia University
FundersAgence Nationale de la Recherche
KeywordsMathematicsPrime (order theory)Integer (computer science)Type (biology)Complex multiplicationAlgebraic numberEisenstein seriesQuadratic fieldAlgebraic number fieldField (mathematics)CombinatoricsAutomorphic formPure mathematicsModular formFunction (biology)Elliptic curveQuadratic equationMathematical analysisGeometryQuadratic function

Abstract

fetched live from OpenAlex

For every triple F , K , p where F is a classical elliptic eigenform, K is a quadratic imaginary field and p is an odd prime integer which is not split in K , we attach p -adic L -function which interpolates the algebraic parts of the special values of the complex L -functions of F twisted by algebraic Hecke characters of K such that the p -part of their conductor is p^{n} , with n large enough (for p\geq 5 it suffices n\ge 2 ). This construction extends a classical construction of N. Katz for F an Eisenstein series, and of Bertolini–Darmon–Prasanna for F a cuspform when p is split in K . Moreover, we prove a Kronecker limit formula, respectively, p -adic Gross–Zagier formulae, for our newly defined p -adic L -functions.

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)0.001
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.436
Threshold uncertainty score0.972

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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 head0.057
GPT teacher head0.372
Teacher spread0.315 · 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