Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 37 min ago
Peer-reviewedCC BY 4.0Polynesian Journal of Mathematics

An introduction to the strategy of transcendence proofs

  • Michel Waldschmidt
Open at sourcePDFDOICite

Abstract

The proof by Ch. Hermite of the transcendence of the number e in 1873 is the model on which most transcendence proofs for constants of analysis are based. The Schneider-Lang Theorem gives an opportunity to understand the strategy behind the proof. We only outline the main ideas, without providing technical details, for which we refer to the bibliography.

Related

  1. Transcendence of dendric beta-expansions with pure discrete spectrum
    Jihyuk Seo, Wolfgang Steiner
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryDynamical systemsarXivHAL
  2. On deciding transcendence of power series
    Alin Bostan, Bruno Salvy, Michael F. Singer
    L'Enseignement MathématiquePeer-reviewedCC BY 4.0Full textGeneral mathematicsHAL
  3. On the finite transcendence of Frobenius traces for abelian varieties over ℚ
    Yuto Tsuruta
    arXivPreprintCC BY-SA 4.0Full textAlgebra & number theoryarXiv
  4. Automorphic Transcendence Degree, Growth, and Skew Normalization
    Dinh Van Hoang, Vo Ngoc Thieu, Phan Thanh Toan
    arXivPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryarXiv
  5. Transcendence of Montgomery Reduction Factor in the Ring of Integers Modulo Infinitely Large Primes
    Tomoki Mihara
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@article{waldschmidt2026introduction,
  title = {{An introduction to the strategy of transcendence proofs}},
  author = {Michel Waldschmidt},
  journal = {Polynesian Journal of Mathematics},
  year = {2026},
  month = sep,
  doi = {10.69763/polyjmath.4.14},
  url = {https://hal.science/hal-05843056v1},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - An introduction to the strategy of transcendence proofs
AU  - Michel Waldschmidt
PY  - 2026
DA  - 2026/09/28
JO  - Polynesian Journal of Mathematics
DO  - 10.69763/polyjmath.4.14
UR  - https://hal.science/hal-05843056v1
AB  - The proof by Ch. Hermite of the transcendence of the number e in 1873 is the model on which most transcendence proofs for constants of analysis are based. The Schneider-Lang Theorem gives an opportunity to understand the strategy behind the proof. We only outline the main ideas, without providing technical details, for which we refer to the bibliography.
SN  - 3075-3422
SN  - 3075-3422
ER  -