Geodesic
Diophantine representation of the decimal expansions of $e$ and $\pi$
Mathematica slovaca, Tome 50 (2000) no. 5, pp. 531-539
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 11A63, 11U05 
@article{MASLO_2000_50_5_a3,
     author = {Baxa, Christoph},
     title = {Diophantine representation of the decimal expansions of $e$ and $\pi$},
     journal = {Mathematica slovaca},
     pages = {531--539},
     year = {2000},
     volume = {50},
     number = {5},
     mrnumber = {1813701},
     zbl = {0984.11007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MASLO_2000_50_5_a3/}
}
TY  - JOUR
AU  - Baxa, Christoph
TI  - Diophantine representation of the decimal expansions of $e$ and $\pi$
JO  - Mathematica slovaca
PY  - 2000
SP  - 531
EP  - 539
VL  - 50
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MASLO_2000_50_5_a3/
LA  - en
ID  - MASLO_2000_50_5_a3
ER  - 
%0 Journal Article
%A Baxa, Christoph
%T Diophantine representation of the decimal expansions of $e$ and $\pi$
%J Mathematica slovaca
%D 2000
%P 531-539
%V 50
%N 5
%U http://geodesic.mathdoc.fr/item/MASLO_2000_50_5_a3/
%G en
%F MASLO_2000_50_5_a3
Baxa, Christoph. Diophantine representation of the decimal expansions of $e$ and $\pi$. Mathematica slovaca, Tome 50 (2000) no. 5, pp. 531-539. http://geodesic.mathdoc.fr/item/MASLO_2000_50_5_a3/

[1] BAILEY D. H.-BORWEIN J. M.-BORWEIN P. B.-PLOUFFE S.: The quest for Pi. Math. Intell. 19 (1997), 50-57. | MR | Zbl

[2] BAXA C.: A note on Diophantine representations. Amer. Math. Monthly 100 (1993), 138-143. | MR | Zbl

[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). | MR

[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.

[5] DAVIS M.-PUТNAM H.-ROBINSON J.: The decision problem for exponential Diphantine equations. Ann. Matһ. 74 (1961), 425-436. | MR

[6] JONES J. P.: Diophantine representation of Mersejine and Fermat primes. Acta Arith. 35 (1979), 209-221. | MR

[7] JONES J. P.: Universal Diophantine equation. J. Symb. Logic 47 (1982), 549-571. | MR | Zbl

[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. | MR | Zbl

[9] JONES J. P.-MAТIJASEVIČ, YU. V.: Proof of recursive unsolvability of Hilberťs Tenth Problem. Amer. Math. Monthly 98 (1991), 689-709. | MR

[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. | MR

[11] MANIN, YU. I.: A Course in Mathematical Logic. Springer, New York, 1977. | MR | Zbl

[12] MATIJASEVIČ, JU. V.: Enumerable sets are Diophantine. Soviet Math. Doklady 11 (1970), 354-358.

[13] MATIJASEVIČ, JU. V.: Diophantine representation of the set of prime numbers. Soviet Math. Doklady 12 (1971), 249-254.

[14] MATIYASEVICH, YU. V.: Hilberťs Tenth Problem. MIT Press, Cambridge-Massachusetts, 1993. | MR

[15] PUTNAM H.: An unsolvable problem in number theory. J. Symb. Logic 25 (1960), 220-232. | MR

[16] SMORYŃSKI C.: Logical Number Theory I. Springer, Berlin, 1991. | MR | Zbl