Diophantine representation of the decimal expansions of e and π

Christoph Baxa

Mathematica Slovaca (2000)

  • Volume: 50, Issue: 5, page 531-539
  • ISSN: 0232-0525

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Baxa, Christoph. "Diophantine representation of the decimal expansions of $e$ and $\pi $." Mathematica Slovaca 50.5 (2000): 531-539. <http://eudml.org/doc/31979>.

@article{Baxa2000,
author = {Baxa, Christoph},
journal = {Mathematica Slovaca},
keywords = {Hilbert's Tenth Problem; Diophantine representation; decimal expansion of },
language = {eng},
number = {5},
pages = {531-539},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Diophantine representation of the decimal expansions of $e$ and $\pi $},
url = {http://eudml.org/doc/31979},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Baxa, Christoph
TI - Diophantine representation of the decimal expansions of $e$ and $\pi $
JO - Mathematica Slovaca
PY - 2000
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 50
IS - 5
SP - 531
EP - 539
LA - eng
KW - Hilbert's Tenth Problem; Diophantine representation; decimal expansion of
UR - http://eudml.org/doc/31979
ER -

References

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  1. BAILEY D. H.-BORWEIN J. M.-BORWEIN P. B.-PLOUFFE S., The quest for Pi, Math. Intell. 19 (1997), 50-57. (1997) Zbl0878.11002MR1439159
  2. BAXA C., A note on Diophantine representations, Amer. Math. Monthly 100 (1993), 138-143. (1993) Zbl0805.11085MR1212399
  3. DAVIS M., Hilberťs Tenth Problem is unsolvable, Amer. Math. Monthly 80 (1973), 233-269 (Reprinted as Appendix 2 in: DAVIS, M.: Computability and Unsolvability, Dover, New York, 1982). (1973) MR0317916
  4. DAVIS M.-MAТIJASEVIČ, YU. V.-ROBINSON J., Hilberťs Tenth Problem. Diophantine equations: Positive aspects of a negative solution, In: Mathematical Developments Arising from Hilbert Problems (F. E. Browder, ed.), Amer. Math. Soc, Providence, RI, 1976. (1976) 
  5. DAVIS M.-PUТNAM H.-ROBINSON J., The decision problem for exponential Diphantine equations, Ann. Matһ. 74 (1961), 425-436. (1961) MR0133227
  6. JONES J. P., Diophantine representation of Mersejine and Fermat primes, Acta Arith. 35 (1979), 209-221. (1979) MR0550293
  7. JONES J. P., Universal Diophantine equation, J. Symb. Logic 47 (1982), 549-571. (1982) Zbl0492.03018MR0666816
  8. JONES J. P.-MAТIJASEVIČ, JU. V., A new representation for the symmetric binomial coefficient and its applications, Ann. Sci. Math. Québec 6 (1982), 81-97. (1982) Zbl0499.03028MR0672122
  9. JONES J. P.-MAТIJASEVIČ, YU. V., Proof of recursive unsolvability of Hilberťs Tenth Problem, Amer. Math. Monthly 98 (1991), 689-709. (1991) MR1130680
  10. JONES J. P.-SAТO D.-WADA H.-WIENS D., Diophantine representatюn of the set of prime numbers, Amer. Math. Monthly 83 (1976), 449-464. (1976) MR0414514
  11. MANIN, YU. I., A Course in Mathematical Logic, Springer, New York, 1977. (1977) Zbl0383.03002MR0457126
  12. MATIJASEVIČ, JU. V., Enumerable sets are Diophantine, Soviet Math. Doklady 11 (1970), 354-358. (1970) 
  13. MATIJASEVIČ, JU. V., Diophantine representation of the set of prime numbers, Soviet Math. Doklady 12 (1971), 249-254. (1971) 
  14. MATIYASEVICH, YU. V., Hilberťs Tenth Problem, MIT Press, Cambridge-Massachusetts, 1993. (1993) MR1244324
  15. PUTNAM H., An unsolvable problem in number theory, J. Symb. Logic 25 (1960), 220-232. (1960) MR0158825
  16. SMORYŃSKI C., Logical Number Theory I, Springer, Berlin, 1991. (1991) Zbl0759.03002MR1106853

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