An introduction to Mahler's method for transcendence and algebraic independence

Federico Pellarin (LAMUSE)

RECORD

An introduction to Mahler's method for transcendence and algebraic independence

Federico Pellarin (LAMUSE)

Number Theory · Submitted 7 May 2010

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

The authors' main claim Here we propose a survey on Mahler's theory for transcendence and algebraic independence focusing on certain applications to the arithmetic of periods of Anderson t-motives.

how it is stated · asserted 0.70 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, 1,622 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

Here we propose a survey on Mahler's theory for transcendence and algebraic independence focusing on certain applications to the arithmetic of periods of Anderson t-motives.

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	Here we propose a survey on Mahler's theory for transcendence and algebraic independence focusing on certain applications to the arithmetic of periods of Anderson t-motives.	contribution 1.00	0.44	0.24	asserted 0.70

What kind of paper the classifier reports this is: review 1.00 · evidence from literature 0.97.

What was examined, and what was not

sources read

arXiv listing abstract v2

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

Here we propose a survey on Mahler's theory for transcendence and algebraic independence focusing on certain applications to the arithmetic of periods of Anderson t-motives.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

3 arXiv papers cite this in 4 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 1 sentence without a confident label

Uses its method or tool 1 paper

Moreover, the use of the functions [equation] satisfying the functional equation $f_t(X)=(1-t/X^q)f_t(X^q)$, the identity $L(χ_t,1)=f_t(θ)/f_θ(θ)$ and Mahler's method for transcendence as in [ref] , allow to show that for all $t$ algebraic non-zero not of the form $θ^q^i$ for $i∈$, $L(χ_t,1)$ and $π$ are algebraically independent.

Values of certain L-series in positive characteristic · Introduction, results · 0.98

Cites it as background 2 papers

Nous rappelons les égalités et inégalités fondamentales suivantes (voir par exemple [ref] ).

M\'ethode de Mahler en caract{\'e}ristique non nulle : un analogue du Th\'eor\`eme de Ku. Nishioka · Extensions finies et formule du produit · 0.96
We refer to Pellarin's introduction [ref] for a historical and tutorial presentation, and to the references therein; see also Nishioka [ref] for a textbook.

Computing solutions of linear Mahler equations · Context · 1.00

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.