On a character sum problem of H. Cohn

Par Kurlberg

RECORD

On a character sum problem of H. Cohn

Par Kurlberg

Number Theory · Submitted 29 Jan 2001

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

The authors' main claim We prove that this is the case for finite fields of prime cardinality under the assumption that the nonzero values of $f$ are roots of unity.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,067 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.92 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.39 · compares with prior results 0.16 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Let $f$ be a complex valued function on a finite field $F$ such that $f(0) = 0$, $f(1) = 1$, and $|f(x)| = 1$ for $x \neq 0$. Cohn asked if it follows that $f$ is a nontrivial multiplicative character provided that $\sum_{x \in F} f(x) \bar{f(x+h)} = -1$ for $h \neq 0$. We prove that this is the case for finite fields of prime cardinality under the assumption that the nonzero values of $f$ are roots of unity.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Let $f$ be a complex valued function on a finite field $F$ such that $f(0) = 0$, $f(1) = 1$, and $\|f(x)\| = 1$ for $x \neq 0$.	background 1.00	0.11	0.02	asserted 0.82
s1	Cohn asked if it follows that $f$ is a nontrivial multiplicative character provided that $\sum_{x \in F} f(x) \bar{f(x+h)} = -1$ for $h \neq 0$.	background 0.99	0.04	0.04	speculative 0.38
s2	We prove that this is the case for finite fields of prime cardinality under the assumption that the nonzero values of $f$ are roots of unity.	result 0.90	0.96	0.96	asserted 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 v1

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

Let $f$ be a complex valued function on a finite field $F$ such that $f(0) = 0$, $f(1) = 1$, and $|f(x)| = 1$ for $x \neq 0$. Cohn asked if it follows that $f$ is a nontrivial multiplicative character provided that $\sum_{x \in F} f(x) \bar{f(x+h)} = -1$ for $h \neq 0$. We prove that this is the case for finite fields of prime cardinality under the assumption that the nonzero values of $f$ are roots of unity.

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.