% Bibliography of paper.tex, for \bibliographystyle{amsplain}.
% Titles carry double braces because amsplain changes the case of a title otherwise.
% amsplain does not print the url field, so a link is also given in howpublished, which it does print.

@book{BW07,
  author    = {A. Baker and G. W\"ustholz},
  title     = {{Logarithmic Forms and Diophantine Geometry}},
  series    = {New Math.\ Monogr.},
  volume    = {9},
  publisher = {Cambridge Univ.\ Press},
  year      = {2007},
}

@article{Be82,
  author  = {D. Bertrand},
  title   = {{Valeurs de fonctions th\^eta et hauteurs $p$-adiques}},
  journal = {Progr.\ Math.},
  volume  = {22},
  year    = {1982},
  pages   = {1--11},
}

@incollection{Be83,
  author    = {D. Bertrand},
  title     = {{Endomorphismes de groupes alg\'ebriques; applications arithm\'etiques}},
  booktitle = {Approximations diophantiennes et nombres transcendants (Luminy 1982)},
  series    = {Progr.\ Math.},
  volume    = {31},
  publisher = {Birkh\"auser},
  year      = {1983},
  pages     = {1--45},
}

@article{BL81,
  author  = {D. Bertrand and M. Laurent},
  title   = {{Propri\'et\'es de transcendance de nombres li\'es aux fonctions th\^eta}},
  journal = {C. R. Acad.\ Sci.\ Paris S\'er.\ I},
  volume  = {292},
  year    = {1981},
  pages   = {747--749},
}

@book{Ch84,
  author    = {G. V. Chudnovsky},
  title     = {{Contributions to the Theory of Transcendental Numbers}},
  series    = {Math.\ Surveys Monogr.},
  volume    = {19},
  publisher = {Amer.\ Math.\ Soc.},
  year      = {1984},
}

@article{Di04,
  author  = {G. Diaz},
  title   = {{Utilisation de la conjugaison complexe dans l'\'etude de la transcendance de valeurs de la fonction exponentielle usuelle}},
  journal = {J. Th\'eor.\ Nombres Bordeaux},
  volume  = {16},
  year    = {2004},
  pages   = {535--553},
}

@article{Di07,
  author  = {G. Diaz},
  title   = {{Produits et quotients de combinaisons lin\'eaires de logarithmes de nombres alg\'ebriques: conjectures et r\'esultats partiels}},
  journal = {J. Th\'eor.\ Nombres Bordeaux},
  volume  = {19},
  year    = {2007},
  pages   = {373--391},
}

@article{Gr78,
  author  = {B. H. Gross},
  title   = {{On the periods of abelian integrals and a formula of Chowla and Selberg}},
  journal = {Invent.\ Math.},
  volume  = {45},
  year    = {1978},
  pages   = {193--211},
  note    = {with an appendix by D. E. Rohrlich},
}

@article{La80,
  author  = {M. Laurent},
  title   = {{Ind\'ependance lin\'eaire de valeurs de fonctions doublement quasi-p\'eriodiques}},
  journal = {C. R. Acad.\ Sci.\ Paris S\'er.~A},
  volume  = {290},
  year    = {1980},
  pages   = {397--399},
}

@article{La82,
  author  = {M. Laurent},
  title   = {{Transcendance de p\'eriodes d'int\'egrales elliptiques II}},
  journal = {J. reine angew.\ Math.},
  volume  = {333},
  year    = {1982},
  pages   = {144--161},
}

@article{W97,
  author  = {M. Waldschmidt},
  title   = {{Sur la nature arithm\'etique des valeurs de fonctions modulaires}},
  journal = {Ast\'erisque},
  volume  = {245},
  year    = {1997},
  pages   = {105--140},
  note    = {S\'eminaire Bourbaki, expos\'e 824},
}

@unpublished{KrR,
  author = {S. Krisman},
  title  = {{The Roy--Waldschmidt theorem with period term and inner weight: a written proof from Waldschmidt's subgroup theorem}},
  note   = {in preparation},
}

@misc{LSG,
  author       = {S. Krisman},
  title        = {{\texttt{waldschmidt-subgroup-theorem}: a Lean formalization of Waldschmidt's subgroup theorem with period term for groups with elliptic factors}},
  howpublished = {\url{https://github.com/telaviv/waldschmidt-subgroup-theorem}},
  url          = {https://github.com/telaviv/waldschmidt-subgroup-theorem},
  note         = {commit adcfce9},
}

@unpublished{KrL,
  author = {S. Krisman},
  title  = {{A Lean formalization of Waldschmidt's subgroup theorem with period term for groups with elliptic factors}},
  note   = {preprint},
  year   = {2026},
}

@misc{LM,
  author       = {S. Krisman},
  title        = {{\texttt{four-exponentials-cm-periods}: a Lean~4 certificate for the statements of this note}},
  howpublished = {\url{https://github.com/telaviv/four-exponentials-cm-periods}},
  url          = {https://github.com/telaviv/four-exponentials-cm-periods},
  note         = {depending on \cite{LSG}, commit a02679d},
}

@book{Ma75,
  author    = {D. W. Masser},
  title     = {{Elliptic Functions and Transcendence}},
  series    = {Lecture Notes in Math.},
  volume    = {437},
  publisher = {Springer},
  year      = {1975},
}

@book{MM74,
  author    = {B. Mazur and W. Messing},
  title     = {{Universal Extensions and One Dimensional Crystalline Cohomology}},
  series    = {Lecture Notes in Math.},
  volume    = {370},
  publisher = {Springer},
  year      = {1974},
}

@article{Ph86,
  author  = {P. Philippon},
  title   = {{Lemmes de z\'eros dans les groupes alg\'ebriques commutatifs}},
  journal = {Bull.\ Soc.\ Math.\ France},
  volume  = {114},
  year    = {1986},
  pages   = {355--383},
  note    = {errata, ibid.\ \textbf{115} (1987), 397--398},
}

@article{Roy92,
  author  = {D. Roy},
  title   = {{Matrices whose coefficients are linear forms in logarithms}},
  journal = {J. Number Theory},
  volume  = {41},
  year    = {1992},
  pages   = {22--47},
}

@incollection{R1,
  author    = {D. Roy},
  title     = {{Transcendance et questions de r\'epartition dans les groupes alg\'ebriques}},
  editor    = {P. Philippon},
  booktitle = {Approximations diophantiennes et nombres transcendants (Luminy 1990)},
  publisher = {de Gruyter},
  year      = {1992},
  pages     = {249--274},
}

@article{RW93,
  author  = {D. Roy and M. Waldschmidt},
  title   = {{Autour du th\'eor\`eme du sous-groupe alg\'ebrique}},
  journal = {Canad.\ Math.\ Bull.},
  volume  = {36},
  year    = {1993},
  pages   = {358--367},
}

@article{Sch37,
  author  = {Th. Schneider},
  title   = {{Arithmetische Untersuchungen elliptischer Integrale}},
  journal = {Math.\ Ann.},
  volume  = {113},
  year    = {1937},
  pages   = {1--13},
}

@book{Sh98,
  author    = {G. Shimura},
  title     = {{Abelian Varieties with Complex Multiplication and Modular Functions}},
  series    = {Princeton Math.\ Ser.},
  volume    = {46},
  publisher = {Princeton Univ.\ Press},
  year      = {1998},
}

@book{W79,
  author = {M. Waldschmidt},
  title  = {{Nombres transcendants et groupes alg\'ebriques}},
  series = {Ast\'erisque},
  volume = {69--70},
  year   = {1979},
  note   = {with appendices by D. Bertrand and J.-P. Serre},
}

@article{W83,
  author  = {M. Waldschmidt},
  title   = {{Sous-groupes analytiques de groupes alg\'ebriques}},
  journal = {Ann.\ of Math.},
  volume  = {117},
  year    = {1983},
  pages   = {627--657},
}

@incollection{W88,
  author    = {M. Waldschmidt},
  title     = {{On the transcendence methods of Gel'fond and Schneider in several variables}},
  editor    = {A. Baker},
  booktitle = {New Advances in Transcendence Theory (Durham 1986)},
  publisher = {Cambridge Univ.\ Press},
  year      = {1988},
  pages     = {375--398},
  note      = {Ch.~24},
}

@incollection{W90,
  author    = {M. Waldschmidt},
  title     = {{Dependence of logarithms of algebraic points}},
  booktitle = {Number Theory, Vol.~II (Budapest 1987)},
  series    = {Colloq.\ Math.\ Soc.\ J\'anos Bolyai},
  volume    = {51},
  publisher = {North-Holland},
  year      = {1990},
  pages     = {1013--1035},
}

@misc{W03s,
  author       = {M. Waldschmidt},
  title        = {{Dependence of logarithms on commutative algebraic groups}},
  howpublished = {slides, International Conference on Algebra and Number Theory, Hyderabad},
  month        = {December},
  year         = {2003},
}

@incollection{W05,
  author    = {M. Waldschmidt},
  title     = {{Variations on the six exponentials theorem}},
  booktitle = {Algebra and Number Theory (Hyderabad 2003)},
  publisher = {Hindustan Book Agency},
  year      = {2005},
  pages     = {338--355},
}

@incollection{W06,
  author    = {M. Waldschmidt},
  title     = {{Elliptic functions and transcendence}},
  booktitle = {Surveys in Number Theory},
  series    = {Dev.\ Math.},
  volume    = {17},
  publisher = {Springer},
  year      = {2008},
  pages     = {143--188},
}

@incollection{W07,
  author    = {M. Waldschmidt},
  title     = {{The role of complex conjugation in transcendental number theory}},
  editor    = {N. Saradha},
  booktitle = {Diophantine Equations (DION 2005, Mumbai)},
  series    = {Tata Inst.\ Fund.\ Res.\ Stud.\ Math.},
  volume    = {20},
  publisher = {Narosa},
  address   = {New Delhi},
  year      = {2008},
  pages     = {297--308},
}

@incollection{W22,
  author    = {M. Waldschmidt},
  title     = {{The four exponentials problem and Schanuel's conjecture}},
  booktitle = {Mathematics Going Forward},
  series    = {Lecture Notes in Math.},
  volume    = {2313},
  publisher = {Springer},
  address   = {Cham},
  year      = {2023},
  pages     = {579--592},
}

@article{We76,
  author  = {A. Weil},
  title   = {{Sur les p\'eriodes des int\'egrales ab\'eliennes}},
  journal = {Comm.\ Pure Appl.\ Math.},
  volume  = {29},
  year    = {1976},
  pages   = {813--819},
}

@article{Wu89,
  author  = {G. W\"ustholz},
  title   = {{Algebraische Punkte auf analytischen Untergruppen algebraischer Gruppen}},
  journal = {Ann.\ of Math.},
  volume  = {129},
  year    = {1989},
  pages   = {501--517},
}