A Problem Concerning a Character Sum (Extended Abstract)
Bibliographic record
Abstract
? ) E. Teske 1 and H.C. Williams ??2 1 Technische Universitat Darmstadt Institut fur Theoretische Informatik Alexanderstrae 10, 64283 Darmstadt Germany 2 University of Manitoba Dept. of Computer Science Winnipeg, MB Canada R3T 2N2 Abstract. Let p be a prime congruent to 1 modulo 4, n p the Legendre symbol and S(k) = P p 1 n=1 n k n p . The problem of nding a prime p such that S(3) > 0 was one of the motivating forces behind the development of several of Shanks' ideas for computing in algebraic number elds, although neither he nor D. H. and Emma Lehmer were ever successful in nding such a p. In this extended abstract we summarize some techniques which were successful in producing, for each k such that 3 k 2000, a value for p such that S(k) > 0. 1 Introduction Let d denote a fundamental discriminant of an imaginary quadratic eld IK = Q( p d ) and let h(d) denote the class number of IK. Let p be a prime ( 3(mod 4)), n p the Legendre symbol and S...
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.019 | 0.004 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".