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The number of linear factors of supersingular polynomials and sporadic simple groups

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Tomoaki Nakaya

Number Theory · Submitted 7 Sep 2018

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

The authors' main claim In this paper, we will present analogous coincidences of supersingular invariants in level 2 and 3 and the orders of the Baby monster group and the Fischer's group.

how it is stated · asserted 0.95 read the record →

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arXiv ID1809.02363 (version 1)
Pith IDP6EHKNRR, Pith's permanent record of this paper and its review
CitationTomoaki Nakaya. "The number of linear factors of supersingular polynomials and sporadic simple groups." arXiv:1809.02363 (2018). https://pith.science/paper/P6EHKNRR
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,630 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.65 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The set of prime numbers $p$ such that the supersingular $j$-invariants in characteristic $p$ are all contained in the prime field is finite. And it is well known that this set of primes coincides with the set of prime divisors of the order of the Monster simple group. In this paper, we will present analogous coincidences of supersingular invariants in level 2 and 3 and the orders of the Baby monster group and the Fischer's group. The proof uses a connection between the number of supersingular invariants and class numbers of imaginary quadratic fields.

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 The set of prime numbers $p$ such that the supersingular $j$-invariants in characteristic $p$ are all contained in the prime field is finite. background 0.92 0.13 0.14 asserted 1.00
s1 And it is well known that this set of primes coincides with the set of prime divisors of the order of the Monster simple group. background 1.00 0.04 0.08 asserted 1.00
s2 In this paper, we will present analogous coincidences of supersingular invariants in level 2 and 3 and the orders of the Baby monster group and the Fischer's group. contribution 0.93 0.83 0.75 asserted 0.95
s3 The proof uses a connection between the number of supersingular invariants and class numbers of imaginary quadratic fields. method 1.00 0.47 0.06 asserted 1.00

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

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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

The set of prime numbers $p$ such that the supersingular $j$-invariants in characteristic $p$ are all contained in the prime field is finite. And it is well known that this set of primes coincides with the set of prime divisors of the order of the Monster simple group. In this paper, we will present analogous coincidences of supersingular invariants in level 2 and 3 and the orders of the Baby monster group and the Fischer's group. The proof uses a connection between the number of supersingular invariants and class numbers of imaginary quadratic fields.

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