@book{silverman,
  author = {Silverman, Joseph H.},
  title = {The Arithmetic of Elliptic Curves},
  edition = {Second},
  series = {Graduate Texts in Mathematics},
  volume = {106},
  publisher = {Springer},
  year = {2009},
  doi = {10.1007/978-0-387-09494-6},
  isbn = {978-0-387-09493-9}
}

@article{mati1970,
  author = {Matiyasevich, Yu. V.},
  title = {The {Diophantineness} of Enumerable Sets},
  journal = {Doklady Akademii Nauk SSSR},
  volume = {191},
  number = {2},
  pages = {279--282},
  year = {1970},
  note = {Russian original},
  url = {https://www.mathnet.ru/eng/dan35274}
}

@article{mati1974,
  author = {Matiyasevich, Yu. V.},
  title = {The Existence of Non-effectivizable Estimates in the Theory of Exponential {Diophantine} Equations},
  journal = {Zapiski Nauchnykh Seminarov LOMI},
  volume = {40},
  pages = {77--93},
  year = {1974},
  note = {Russian original},
  url = {https://www.mathnet.ru/eng/znsl2683}
}

@article{mati2010,
  author = {Matiyasevich, Yu.},
  title = {Towards Finite-fold {Diophantine} Representations},
  journal = {Zapiski Nauchnykh Seminarov POMI},
  volume = {377},
  pages = {78--90},
  year = {2010},
  url = {https://www.mathnet.ru/eng/znsl3816}
}

@article{dpr1961,
  author = {Davis, Martin and Putnam, Hilary and Robinson, Julia},
  title = {The Decision Problem for Exponential {Diophantine} Equations},
  journal = {Annals of Mathematics},
  series = {2},
  volume = {74},
  number = {3},
  pages = {425--436},
  year = {1961},
  doi = {10.2307/1970289}
}

@article{minsky1961,
  author = {Minsky, Marvin L.},
  title = {Recursive Unsolvability of {Post}'s Problem of ``Tag'' and Other Topics in Theory of {Turing} Machines},
  journal = {Annals of Mathematics},
  series = {2},
  volume = {74},
  number = {3},
  pages = {437--455},
  year = {1961},
  doi = {10.2307/1970290}
}

@article{shepherdson1963,
  author = {Shepherdson, J. C. and Sturgis, H. E.},
  title = {Computability of Recursive Functions},
  journal = {Journal of the ACM},
  volume = {10},
  number = {2},
  pages = {217--255},
  year = {1963},
  doi = {10.1145/321160.321170}
}

@article{cco2024,
  author = {Cantone, D. and Cuzziol, L. and Omodeo, E. G.},
  title = {On {Diophantine} Singlefold Specifications},
  journal = {Le Matematiche},
  volume = {79},
  number = {2},
  pages = {585--620},
  year = {2024},
  doi = {10.4418/2024.79.2.18}
}

@article{jm1984,
  author = {Jones, J. P. and Matiyasevich, Yu. V.},
  title = {Register Machine Proof of the Theorem on Exponential {Diophantine} Representation of Enumerable Sets},
  journal = {Journal of Symbolic Logic},
  volume = {49},
  number = {3},
  pages = {818--829},
  year = {1984},
  doi = {10.2307/2274135}
}

@article{jm1991,
  author = {Jones, J. P. and Matiyasevich, Yu. V.},
  title = {Proof of Recursive Unsolvability of {Hilbert}'s Tenth Problem},
  journal = {American Mathematical Monthly},
  volume = {98},
  number = {8},
  pages = {689--709},
  year = {1991},
  doi = {10.2307/2324421}
}

@book{chaitin1987,
  author = {Chaitin, Gregory J.},
  title = {Algorithmic Information Theory},
  series = {Cambridge Tracts in Theoretical Computer Science},
  volume = {1},
  publisher = {Cambridge University Press},
  year = {1987},
  note = {Revised third printing, 1990},
  doi = {10.1017/CBO9780511608858}
}

@incollection{poonen2002,
  author = {Poonen, Bjorn},
  title = {Using Elliptic Curves of Rank One towards the Undecidability of {Hilbert}'s Tenth Problem over Rings of Algebraic Integers},
  booktitle = {Algorithmic Number Theory},
  editor = {Fieker, Claus and Kohel, David R.},
  series = {Lecture Notes in Computer Science},
  volume = {2369},
  pages = {33--42},
  publisher = {Springer},
  year = {2002},
  url = {https://math.mit.edu/~poonen/papers/ants5.pdf}
}

@article{millershlapentokh2022,
  author = {Miller, Russell and Shlapentokh, Alexandra},
  title = {On Existential Definitions of C.E. Subsets of Rings of Functions of Characteristic 0},
  journal = {Annals of Pure and Applied Logic},
  volume = {173},
  number = {4},
  pages = {103076},
  year = {2022},
  doi = {10.1016/j.apal.2021.103076}
}

@article{lucas1878,
  author = {Lucas, {\'E}douard},
  title = {Sur les congruences des nombres eul{\'e}riens et des coefficients
    diff{\'e}rentiels des fonctions trigonom{\'e}triques suivant un module premier},
  journal = {Bulletin de la Soci{\'e}t{\'e} Math{\'e}matique de France},
  volume = {6},
  year = {1878},
  pages = {49--54},
  doi = {10.24033/bsmf.127}
}

@article{robinson1952,
  author = {Robinson, Julia},
  title = {Existential Definability in Arithmetic},
  journal = {Transactions of the American Mathematical Society},
  volume = {72},
  number = {3},
  year = {1952},
  pages = {437--449},
  doi = {10.1090/S0002-9947-1952-0048374-2}
}
