| Title:
|
Diophantine representation of the decimal expansions of $e$ and $\pi$ (English) |
| Author:
|
Baxa, Christoph |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
50 |
| Issue:
|
5 |
| Year:
|
2000 |
| Pages:
|
531-539 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11A63 |
| MSC:
|
11U05 |
| idZBL:
|
Zbl 0984.11007 |
| idMR:
|
MR1813701 |
| . |
| Date available:
|
2009-09-25T11:47:40Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/130373 |
| . |
| Reference:
|
[1] BAILEY D. H.-BORWEIN J. M.-BORWEIN P. B.-PLOUFFE S.: The quest for Pi.Math. Intell. 19 (1997), 50-57. Zbl 0878.11002, MR 1439159 |
| Reference:
|
[2] BAXA C.: A note on Diophantine representations.Amer. Math. Monthly 100 (1993), 138-143. Zbl 0805.11085, MR 1212399 |
| Reference:
|
[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 0317916 |
| Reference:
|
[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. |
| Reference:
|
[5] DAVIS M.-PUТNAM H.-ROBINSON J.: The decision problem for exponential Diphantine equations.Ann. Matһ. 74 (1961), 425-436. MR 0133227 |
| Reference:
|
[6] JONES J. P.: Diophantine representation of Mersejine and Fermat primes.Acta Arith. 35 (1979), 209-221. MR 0550293 |
| Reference:
|
[7] JONES J. P.: Universal Diophantine equation.J. Symb. Logic 47 (1982), 549-571. Zbl 0492.03018, MR 0666816 |
| Reference:
|
[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. Zbl 0499.03028, MR 0672122 |
| Reference:
|
[9] JONES J. P.-MAТIJASEVIČ, YU. V.: Proof of recursive unsolvability of Hilberťs Tenth Problem.Amer. Math. Monthly 98 (1991), 689-709. MR 1130680 |
| Reference:
|
[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 0414514 |
| Reference:
|
[11] MANIN, YU. I.: A Course in Mathematical Logic.Springer, New York, 1977. Zbl 0383.03002, MR 0457126 |
| Reference:
|
[12] MATIJASEVIČ, JU. V.: Enumerable sets are Diophantine.Soviet Math. Doklady 11 (1970), 354-358. |
| Reference:
|
[13] MATIJASEVIČ, JU. V.: Diophantine representation of the set of prime numbers.Soviet Math. Doklady 12 (1971), 249-254. |
| Reference:
|
[14] MATIYASEVICH, YU. V.: Hilberťs Tenth Problem.MIT Press, Cambridge-Massachusetts, 1993. MR 1244324 |
| Reference:
|
[15] PUTNAM H.: An unsolvable problem in number theory.J. Symb. Logic 25 (1960), 220-232. MR 0158825 |
| Reference:
|
[16] SMORYŃSKI C.: Logical Number Theory I.Springer, Berlin, 1991. Zbl 0759.03002, MR 1106853 |
| . |
