Prime Numbers
Prime Numbers Prime Numbers
558 REFERENCES [Goldwasser and Kilian 1986] S. Goldwasser and J. Kilian. Almost all primes can be quickly certified. In Proc. 18th Annual ACM Symposium on the Theory of Computing, pages 316–329, 1986. [Goldwasser and Micali 1982] S. Goldwasser and S. Micali. Probabilistic encryption and how to play mental poker keeping secret all mental information. In Proc. 14th Annual ACM Symposium on the Theory of Computing, pages 365–377, 1982. [Golomb 1956] S. Golomb. Combinatorial proof of Fermat’s ‘little theorem’. Amer. Math. Monthly, 63, 1956. [Golomb 1982] S. Golomb. Shift Register Sequences, (revised version). Aegean Park Press, 1982. [Gong et al. 1999] G. Gong, T. Berson, and D. Stinson. Elliptic curve pseudorandom sequence generators. In Proc. Sixth Annual Workshop on Selected Areas in Cryptography, Kingston, Canada, August 1999. [Gordon 1993] D. Gordon. Discrete logarithms in GF (p) via the number field sieve. SIAM J. Discrete Math., 16:124–138, 1993. [Gordon and Pomerance 1991] D. Gordon and C. Pomerance. The distribution of Lucas and elliptic pseudoprimes. Math. Comp., 57:825–838, 1991. Corrigendum ibid. 60:877, 1993. [Gordon and Rodemich 1998] D. Gordon and G. Rodemich. Dense admissible sets. In [Buhler 1998], pages 216–225. [Gourdon and Sebah 2004] X. Gourdon and P. Sebah. Numbers, constants and computation, 2004. http://numbers.computation.free.fr/Constants/constants.html. [Graham and Kolesnik 1991] S. Graham and G. Kolesnik. Van der Corput’s method of exponential sums, volume 126 of Lecture Note Series. Cambridge University Press, 1991. [Grantham 1998] J. Grantham. A probable prime test with high confidence. J. Number Theory, 72:32–47, 1998. [Grantham 2001] J. Grantham. Frobenius pseudoprimes. Math. Comp. 70:873–891, 2001. [Granville 2004a] A. Granville. It is easy to determine if a given number is prime. Bull. Amer. Math. Soc., 42:3–38, 2005. [Granville 2004b] A. Granville. Smooth numbers: computational number theory and beyond. In J. Buhler and P. Stevenhagen, editors Cornerstones in algorithmic number theory (tentative title), a Mathematical Sciences Research Institute Publication. Cambridge University Press, to appear. [Granville and Tucker 2002] A. Granville and T. Tucker. It’s as easy as abc. Notices Amer. Math. Soc. 49:1224–1231, 2002. [Green and Tao 2004] B. Green and T. Tao. The primes contain arbitrarily long arithmetic progressions. http://arxiv.org/abs/math.NT/0404188.
REFERENCES 559 [Guy 1976] R. Guy. How to factor a number. In Proceedings of the Fifth Manitoba Conference on Numerical Mathematics (Univ. Manitoba, Winnipeg, Man., 1975), volume 16 of Congressus Numerantium, pages 49–89, 1976. [Guy 1994] R. Guy. Unsolved Problems in Number Theory. Second edition, volume I of Problem Books in Mathematics. Unsolved Problems in Intuitive Mathematics. Springer—Verlag, 1994. [Hafner and McCurley 1989] J. Hafner and K. McCurley. A rigorous subexponential algorithm for computation of class groups. J. Amer. Math. Soc., 2:837–850, 1989. [Halberstam and Richert 1974] H. Halberstam and H.-E. Richert. Sieve Methods, volume 4 of London Mathematical Society Monographs. Academic Press, 1974. [Hardy 1966] G. Hardy. Collected Works of G. H. Hardy, Vol. I. Clarendon Press, Oxford, 1966. [Hardy and Wright 1979] G. Hardy and E. Wright. An Introduction to the Theory of Numbers. Fifth edition. Clarendon Press, Oxford, 1979. [Harley 2002] R. Harley. Algorithmique avancée sur les courbes elliptiques. PhD thesis, University Paris 7, 2002. [H˚astad et al. 1999] J. H˚astad, R. Impagliazzo, L. Levin, and M. Luby. A pseudorandom generator from any one-way function. SIAM J. Computing, 28:1364–1396, 1999. [Hensley and Richards 1973] D. Hensley and I. Richards. Primes in intervals. Acta Arith., 25:375–391, 1973/74. [Hey 1999] T. Hey. Quantum computing. Computing and Control Engineering, 10(3):105–112, 1999. [Higham 1996] N. Higham. Accuracy and Stability of Numerical Algorithms. SIAM, 1996. [Hildebrand 1988a] A. Hildebrand. On the constant in the Pólya–Vinogradov inequality. Canad. Math. Bull., 31:347–352, 1988. [Hildebrand 1988b] A. Hildebrand. Large values of character sums. J. Number Theory, 29:271–296, 1988. [Honaker 1998] G. Honaker, 1998. Private communication. [Hooley 1976] C. Hooley. Applications of Sieve Methods to the Theory of Numbers, volume 70 of Cambridge Tracts in Mathematics. Cambridge University Press, 1976. [Ivić 1985] A. Ivić. The Riemann Zeta-Function. John Wiley and Sons, 1985. [Izu et al. 1998] T. Izu, J. Kogure, M. Noro, and K. Yokoyama. Efficient implementation of Schoof’s algorithm. In Advances in Cryptology, Proc. Asiacrypt ’98, volume 1514 of Lecture Notes in Computer Science, pages 66–79. Springer—Verlag, 1998. [Jaeschke 1993] G. Jaeschke. On strong pseudoprimes to several bases. Math. Comp., 61:915–926, 1993.
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- Page 556 and 557: 548 REFERENCES [Apostol 1986] T. Ap
- Page 558 and 559: 550 REFERENCES [Bernstein 2004b] D.
- Page 560 and 561: 552 REFERENCES [Buchmann et al. 199
- Page 562 and 563: 554 REFERENCES [Crandall 1997b] R.
- Page 564 and 565: 556 REFERENCES [Dudon 1987] J. Dudo
- Page 568 and 569: 560 REFERENCES [Joe 1999] S. Joe. A
- Page 570 and 571: 562 REFERENCES [Lenstra 1981] H. Le
- Page 572 and 573: 564 REFERENCES [Montgomery 1987] P.
- Page 574 and 575: 566 REFERENCES [Oesterlé 1985] J.
- Page 576 and 577: 568 REFERENCES [Pomerance et al. 19
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- Page 582 and 583: 574 REFERENCES [Weisstein 2005] E.
- Page 584 and 585: Index ABC conjecture, 417, 434 abel
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- Page 590 and 591: INDEX 583 complex-field, 477 Cooley
- Page 592 and 593: INDEX 585 Hajratwala, N., 23 Halber
- Page 594 and 595: INDEX 587 Lehmer, D., 149, 152, 155
- Page 596 and 597: INDEX 589 432, 447-450, 453, 458, 5
- Page 598 and 599: INDEX 591 Preneel, B. (with De Win
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REFERENCES 559<br />
[Guy 1976] R. Guy. How to factor a number. In Proceedings of the Fifth Manitoba<br />
Conference on Numerical Mathematics (Univ. Manitoba, Winnipeg, Man.,<br />
1975), volume 16 of Congressus Numerantium, pages 49–89, 1976.<br />
[Guy 1994] R. Guy. Unsolved Problems in Number Theory. Second edition,<br />
volume I of Problem Books in Mathematics. Unsolved Problems in<br />
Intuitive Mathematics. Springer—Verlag, 1994.<br />
[Hafner and McCurley 1989] J. Hafner and K. McCurley. A rigorous<br />
subexponential algorithm for computation of class groups. J. Amer.<br />
Math. Soc., 2:837–850, 1989.<br />
[Halberstam and Richert 1974] H. Halberstam and H.-E. Richert. Sieve Methods,<br />
volume 4 of London Mathematical Society Monographs. Academic Press,<br />
1974.<br />
[Hardy 1966] G. Hardy. Collected Works of G. H. Hardy, Vol. I. Clarendon Press,<br />
Oxford, 1966.<br />
[Hardy and Wright 1979] G. Hardy and E. Wright. An Introduction to the Theory<br />
of <strong>Numbers</strong>. Fifth edition. Clarendon Press, Oxford, 1979.<br />
[Harley 2002] R. Harley. Algorithmique avancée sur les courbes elliptiques. PhD<br />
thesis, University Paris 7, 2002.<br />
[H˚astad et al. 1999] J. H˚astad, R. Impagliazzo, L. Levin, and M. Luby. A<br />
pseudorandom generator from any one-way function. SIAM J.<br />
Computing, 28:1364–1396, 1999.<br />
[Hensley and Richards 1973] D. Hensley and I. Richards. <strong>Prime</strong>s in intervals. Acta<br />
Arith., 25:375–391, 1973/74.<br />
[Hey 1999] T. Hey. Quantum computing. Computing and Control Engineering,<br />
10(3):105–112, 1999.<br />
[Higham 1996] N. Higham. Accuracy and Stability of Numerical Algorithms.<br />
SIAM, 1996.<br />
[Hildebrand 1988a] A. Hildebrand. On the constant in the Pólya–Vinogradov<br />
inequality. Canad. Math. Bull., 31:347–352, 1988.<br />
[Hildebrand 1988b] A. Hildebrand. Large values of character sums. J. Number<br />
Theory, 29:271–296, 1988.<br />
[Honaker 1998] G. Honaker, 1998. Private communication.<br />
[Hooley 1976] C. Hooley. Applications of Sieve Methods to the Theory of <strong>Numbers</strong>,<br />
volume 70 of Cambridge Tracts in Mathematics. Cambridge University<br />
Press, 1976.<br />
[Ivić 1985] A. Ivić. The Riemann Zeta-Function. John Wiley and Sons, 1985.<br />
[Izu et al. 1998] T. Izu, J. Kogure, M. Noro, and K. Yokoyama. Efficient<br />
implementation of Schoof’s algorithm. In Advances in Cryptology, Proc.<br />
Asiacrypt ’98, volume 1514 of Lecture Notes in Computer Science, pages<br />
66–79. Springer—Verlag, 1998.<br />
[Jaeschke 1993] G. Jaeschke. On strong pseudoprimes to several bases. Math.<br />
Comp., 61:915–926, 1993.
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