MSC2020 · 11Jxx

Diophantine approximation, transcendental number theory

Diophantine approximation, transcendental number theory [See also 11K60]

5 mapped entries · Browse and filter all →

Counts include all statuses and descendants. Classifications are editorial or inferred from community fields, not an AMS assessment of the problem.

Subcategories

11J04Homogeneous approximation to one number0 11J06Markov and Lagrange spectra and generalizations0 11J13Simultaneous homogeneous approximation, linear forms1 11J17Approximation by numbers from a fixed field0 11J20Inhomogeneous linear forms0 11J25Diophantine inequalities0 11J54Small fractional parts of polynomials and generalizations0 11J61Approximation in non-Archimedean valuations0 11J68Approximation to algebraic numbers0 11J70Continued fractions and generalizations1 11J71Distribution modulo one0 11J72Irrationality; linear independence over a field1 11J81Transcendence (general theory)0 11J82Measures of irrationality and of transcendence2 11J83Metric theory0 11J85Algebraic independence; Gel'fond's method0 11J86Linear forms in logarithms; Baker's method0 11J87Schmidt Subspace Theorem and applications0 11J89Transcendence theory of elliptic and abelian functions0 11J91Transcendence theory of other special functions0 11J93Transcendence theory of Drinfel'd and

t

-modules0 11J95Results involving abelian varieties0 11J97Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.)0 11J99Diophantine approximation, transcendental number theory0

Mapped problems

OP-12072Number theoryOpen

Zaremba’s conjecture constant ( $C_{58}$ )

Zaremba’s conjecture constant: determine C 58 or improve its bounds; the repository records 5 (lower) and infty (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-12005Number theoryOpen

Irrationality measure of $\Gamma(1/4)$ ( $C_{7b}$ )

Irrationality measure of Gamma(1/4) : determine C 7b or improve its bounds; the repository records 2 (lower) and 10^ 143 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-12004Number theoryOpen

Irrationality measure of $\pi$ ( $C_{7a}$ )

Irrationality measure of pi : determine C 7a or improve its bounds; the repository records 2 (lower) and 7.103205334137 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-11969Number theoryOpen

The Lonely Runner Conjecture

The Lonely Runner Conjecture. Major advance problem from Epoch AI’s FrontierMath: Open Problems; answers are checked by a verifier program.

Epoch AI — FrontierMath: Open Problems· Licensed source statement· 2026

OP-11942Number theorySolved

Apéry-Style Irrationality Proofs via Linear Recurrences

Apéry-Style Irrationality Proofs via Linear Recurrences. Breakthrough problem from Epoch AI’s FrontierMath: Open Problems; answers are checked by a verifier program.

Epoch AI — FrontierMath: Open Problems· Licensed source statement· 2026

Journals & articles in MSC 11

These are selected sources for the parent class. Article coverage is a first reviewed selection, and may not cover this exact subcategory.

Algebra & Number Theory ↗

Mathematical Sciences Publishers

Algebra, number theory and their connections

EMS Surveys in Mathematical Sciences ↗

European Mathematical Society / EMS Press

Mathematical surveys

Current trends and open problems in arithmetic dynamics
2019 · 3 questions extracted

View source evidence →

Subcategories

Mapped problems

Zaremba’s conjecture constant (C58C_{58}C58​)

Irrationality measure of Γ(1/4)\Gamma(1/4)Γ(1/4) (C7bC_{7b}C7b​)

Irrationality measure of π\piπ (C7aC_{7a}C7a​)

The Lonely Runner Conjecture

Apéry-Style Irrationality Proofs via Linear Recurrences

Journals & articles in MSC 11

Zaremba’s conjecture constant ( $C_{58}$ )

Irrationality measure of $\Gamma(1/4)$ ( $C_{7b}$ )

Irrationality measure of $\pi$ ( $C_{7a}$ )