Title:
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Prvočísla obsahují libovolně dlouhé aritmetické posloupnosti (Czech) |
Title:
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Prime numbers contain arbitrarily long arithmetical progressions (English) |
Author:
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Klazar, Martin |
Language:
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Czech |
Journal:
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Pokroky matematiky, fyziky a astronomie |
ISSN:
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0032-2423 |
Volume:
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49 |
Issue:
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3 |
Year:
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2004 |
Pages:
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177-188 |
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Category:
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math |
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Keyword:
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prime number |
Keyword:
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arithmetic progression |
MSC:
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11A41 |
MSC:
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11N05 |
MSC:
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11N13 |
idZBL:
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Zbl 1265.11089 |
. |
Date available:
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2010-12-11T20:34:06Z |
Last updated:
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2015-11-29 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/141227 |
. |
Reference:
|
[1] Agrawal, M., Kayal, N., Saxena, N.: PRIMES is in P.http://www.cse.iitk.ac.in/news/primality.html Zbl 1071.11070 |
Reference:
|
[2] Bečvářová, M.: Eukleidovy Základy. Jejich vydání a překlady.Prometheus, Praha 2002. Zbl 1024.01030, MR 1929927 |
Reference:
|
[3] Brun, V.: Le crible d’Eratosthène et le théorème de Goldbach.C. R. Acad. Sci. Paris 168 (1919), 544–546. |
Reference:
|
[4] Crandall, R., Pomerance, C.: Prime Numbers. A Computational Perspective.Springer-Verlag, New York 2001. MR 1821158 |
Reference:
|
[5] Davis, M.: Hilbert’s tenth problem is unsolvable.Amer. Math. Monthly 80 (1973), 233–269. MR 0317916, 10.2307/2318447 |
Reference:
|
[6] Dirichlet, P. G. L.: Beweis des Satzes, daß jede unbegrenzte aritmetische Progression, deren erstes Glied und Differenz ganze Zahlen ohne gemeinschaftlichen Factor sind, unendlich viele Primzahlen enthält.Abh. Akad. Berlin (1837), 45–71. |
Reference:
|
[7] Edwards, H. M.: Riemann’s zeta function.Academic Press, New York-London 1974. Zbl 0315.10035, MR 0466039 |
Reference:
|
[8] Edwards, H. M.: Fermat’s last theorem. A genetic introduction to algebraic number theory.Springer-Verlag, New York 1977. Zbl 0355.12001, MR 0616635 |
Reference:
|
[9] Erdős, P.: On a new method in elementary number theory which leads to an elementary proof of the prime number theorem.Proc. Nat. Acad. Sci. U. S. A. 35 (1949), 374–384. MR 0029411, 10.1073/pnas.35.7.374 |
Reference:
|
[10] Friedlander, J., Iwaniec, H.: The polynomial ${X^2+Y^4}$ captures its primes.Ann. of Math. (2) 148 (1998), 945–1040. MR 1670065 |
Reference:
|
[11] Friedlander, J., Iwaniec, H.: Asymptotic sieve for primes.Ann. of Math. (2) 148 (1998), 1041–1065. Zbl 0926.11067, MR 1670069 |
Reference:
|
[12] Furstenberg, H.: Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions.J. Analyse Math. 31 (1977), 204–256. Zbl 0347.28016, MR 0498471 |
Reference:
|
[13] Furstenberg, H., Katznelson, Y., Ornstein, D.: The ergodic theoretical proof of Szemerédi’s theorem.Bull. Amer. Math. Soc. (N. S.) 7 (1982), 527–552. MR 0670131, 10.1090/S0273-0979-1982-15052-2 |
Reference:
|
[14] Goldstein, L. J.: A history of the prime number theorem.Amer. Math. Monthly 80 (1973), 599–615. Zbl 0272.10001, MR 0313171, 10.2307/2319162 |
Reference:
|
[15] Goldston, D., Yildirim, C. Y.: Higher correlations of divisor sums related to primes, I: Triple correlations.Integers 3 (2003), 66 s. Zbl 1118.11039, MR 1985667 |
Reference:
|
[16] Goldston, D., Yildirim, C. Y.: Higher correlations of divisor sums related to primes, III: $k$-correlations.arXiv:math.NT/0209102, 32 s. |
Reference:
|
[17] Goldston, D., Yildirim, C. Y.: Small gaps between primes.Preprint. |
Reference:
|
[18] Gowers, W. T.: A new proof of Szemerédi’s theorem.Geom. Funct. Anal. 11 (2001), 465–588. Zbl 1028.11005, MR 1844079, 10.1007/s00039-001-0332-9 |
Reference:
|
[19] Gowers, T.: Vinogradov’s Three-Primes Theorem.17 s. http://www.dpmms.cam.ac.uk/~wtg10/ |
Reference:
|
[20] Greaves, G.: Sieves in number theory.Springer-Verlag, Berlin 2001. Zbl 1003.11044, MR 1836967 |
Reference:
|
[21] Green, B., Tao, T.: The primes contain arbitrarily long arithmetic progressions.arXiv:math.NT/0404188 (verze 1 z 8. dubna 2004), 49 s. MR 2415379 |
Reference:
|
[22] Heath-Brown, D. R.: Primes represented by ${x^3+2y^3}$.Acta Math. 186 (2001), 1–84. Zbl 1007.11055, MR 1828372, 10.1007/BF02392715 |
Reference:
|
[23] Chen, J.: On the representation of a large even integer as the sum of a prime and the product of at most two primes.Kexue Tongbao 17 (1966), 385–386. MR 0207668 |
Reference:
|
[24] Chen, J.: On the representation of a large even integer as the sum of a prime and the product of at most two primes.Sci. Sinica 16 (1973), 157–176. MR 0434997 |
Reference:
|
[25] Křížek, M.: Od Fermatových prvočísel ke geometrii.In: Šolcová, A., Křížek, M., Mink, G., editoři, Matematik Pierre de Fermat. Cahiers du CEFRES č. 28, 131–161. CEFRES, Praha 2002. |
Reference:
|
[26] Křížek, M., Luca, F., Somer, L.: 17 lectures on Fermat numbers. From number theory to geometry.Springer-Verlag, New York 2001. Zbl 1010.11002, MR 1866957 |
Reference:
|
[27] Kučera, L.: Kombinatorické algoritmy.SNTL, Praha 1983. |
Reference:
|
[28] Levinson, N.: A motivated account of an elementary proof of the prime number theorem.Amer. Math. Monthly 76 (1969), 225–245. Zbl 0172.06001, MR 0241372, 10.2307/2316361 |
Reference:
|
[29] Matijasevič, Ju. V.: Diofantovosť perečislimych množestv.Dokl. Akad. Nauk SSSR 191 (1970), 279–282. |
Reference:
|
[30] Matijasevič, Ju. V.: Diofantovo predstavlenie množestva prostych čisel.Dokl. Akad. Nauk SSSR 196 (1971), 770–773. |
Reference:
|
[31] Matijasevič, Ju. V.: Hilbert’s tenth problem.MIT Press, Cambridge, MA 1993. |
Reference:
|
[32] Nathanson, M. B.: Additive Number Theory. The Classical Bases.Springer-Verlag, New York 1996. Zbl 0859.11002, MR 1395371 |
Reference:
|
[33] Nathanson, M. B.: Elementary Methods in Number Theory.Springer-Verlag, New York 2000. Zbl 0953.11002, MR 1732941 |
Reference:
|
[34] Novák, B.: O elementárním důkazu prvočíselné věty.Časopis pro pěstování matematiky 100 (1975), 71–84. |
Reference:
|
[35] Papadimitriou, Ch. H.: Computational Complexity.Addison-Wesley, Reading, MA 1994. Zbl 0833.68049, MR 1251285 |
Reference:
|
[36] Porubský, Š.: Fermat a teorie čísel.In: Šolcová, A., Křížek, M., Mink, G., editoři, Matematik Pierre de Fermat. Cahiers du CEFRES č. 28, 49–86. CEFRES, Praha 2002. |
Reference:
|
[37] Pratt, V. R.: Every prime has a succinct certificate.SIAM J. Comput. 4 (1975), 214–220. Zbl 0316.68031, MR 0391574, 10.1137/0204018 |
Reference:
|
[38] Rabin, M. O.: Probabilistic Algorithms..In: J. F. Traub, editor, Algorithms and Complexity, 21–39. Academic Press, New York 1976. Zbl 0384.60001, MR 0464678 |
Reference:
|
[39] Riemann, B.: Über die Anzahl der Primzahlen unter einer gegebenen Grösse.Monatsberichte der Berliner Akademie (1859), 671–680. |
Reference:
|
[40] Rivest, R., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems.Comm. ACM 21 1978, 120–126. Zbl 0368.94005, MR 0700103, 10.1145/359340.359342 |
Reference:
|
[41] Selberg, A.: An elementary proof of the prime-number theorem.Ann. of Math. (2) 50 (1949), 305–313. Zbl 0036.30604, MR 0029410, 10.2307/1969455 |
Reference:
|
[42] Serre, J.-P.: A Course in Arithmetics.Springer-Verlag, New York 1973. MR 0344216 |
Reference:
|
[43] Shor, P.: Algorithms for quantum computation: discrete logarithms and factoring.In: 35th Annual Symposium on Foundations of Computer Science (Santa Fe, NM, 1994), 124–134. IEEE Comput. Soc. Press, Los Alamitos, CA 1994. MR 1489242 |
Reference:
|
[44] Schnirelmann, L.: Über additive Eigenschaften von Zahlen.Mat. Ann. 107 (1933), 649–690. Zbl 0006.10402, MR 1512821, 10.1007/BF01448914 |
Reference:
|
[45] Stillwell, J.: Elements of algebra. Geometry, numbers, equations.Springer-Verlag, New York 1994. Zbl 0832.00001, MR 1311026 |
Reference:
|
[46] Szemerédi, E.: On sets of integers containing no $k$ elements in arithmetic progression.Acta Arith. 27 (1975), 199–245. MR 0369312 |
Reference:
|
[47] Šnireľman, L. G.: Ob additivnych svojstvach čisel.Izvestija donskogo politechničeskogo instituta v Novočerkasske 14 (1930), 3–28. |
Reference:
|
[48] Tao, T.: A quantitative ergodic theory proof of Szemerédi’s theorem.arXiv:math.CO/0405251, 51 s. Zbl 1127.11011 |
Reference:
|
[49] Tao, T.: A quantitative ergodic theory proof of Szemerédi’s theorem (abridged).20 s. http://www.math.ucla.edu/~tao/preprints/ |
Reference:
|
[50] Tao, T.: A bound for progressions of length $k$ in the primes.4 s. http://www.math.ucla.edu/~tao/preprints/ |
Reference:
|
[51] Tao, T.: A remark on Goldston-Yildirim correlation estimates.8 s. http://www.math.ucla.edu/~tao/preprints/ |
Reference:
|
[52] Tenenbaum, G.: Introduction to analytic and probabilistic number theory.Cambridge University Press, Cambridge, U. K. 1995. Zbl 0880.11001, MR 1342300 |
Reference:
|
[53] Vinogradov, I. M.: Predstavlenie něčotnogo čisla summoj trjoch prostych čisel.Dokl. Akad. Nauk SSSR 15 (1937), 291–294. |
Reference:
|
[54] Zagier, D.: Newman’s short proof of the prime number theorem.Amer. Math. Monthly 104 (1997), 705–708. Zbl 0887.11039, MR 1476753, 10.2307/2975232 |
Reference:
|
[55] : .http://www.arxiv.org/ |
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