Prime Numbers
Prime Numbers Prime Numbers
550 REFERENCES [Bernstein 2004b] D. Bernstein. Factorization myths. http://cr.yp.to/talks.html#2004.06.14. [Bernstein 2004c] D. Bernstein. Doubly focused enumeration of locally square polynomial values. In High primes and misdemeanours: lectures in honour of the 60th birthday of Hugh Cowie Williams, volume 41 of Fields Inst. Commun., pages 69–76. Amer. Math. Soc., 2004. [Bernstein 2004d] D Bernstein. How to find smooth parts of integers. http://cr.yp.to/papers.html#smoothparts. [Bernstein 2004e] D. Bernstein. Fast multiplication and its applications. 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. [Berrizbeitia 2002] P. Berrizbeitia. Sharpening “PRIMES is in P” for a large family of numbers. http://arxiv.org/find/grp math/1/au:+Berrizbeitia/0/1/0/all/0/1. [Berry 1997] M. Berry. Quantum chaology. Proc. Roy. Soc. London Ser. A, 413:183–198, 1987. [Berta and Mann 2002] I. Berta and Z. Mann. Implementing elliptic-curve cryptography on PC and Smart Card. Periodica Polytechnica, Series Electrical Engineering, 46:47–73, 2002. [Beukers 2004] F. Beukers. The diophantine equation Ax p + By q = Cz r . http://www.math.uu.nl/people/beukers/Fermatlectures.pdf. [Blackburn and Teske 1999] S. Blackburn and E. Teske. Baby-step giant-step algorithms for non-uniform distributions. Unpublished manuscript, 1999. [Bleichenbacher 1996] D. Bleichenbacher. Efficiency and security of cryptosystems based on number theory. PhD thesis, Swiss Federal Institute of Technology Zürich, 1996. [Blum et al. 1986] L. Blum, M. Blum, and M. Shub. A simple unpredictable pseudorandom number generator. SIAM J. Comput., 15:364–383, 1986. [Bombieri and Iwaniec 1986] E. Bombieri and H. Iwaniec. On the order of ζ(1/2+it). Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 13:449–472, 1986. [Bombieri and Lagarias 1999] E. Bombieri and J. Lagarias. Complements to Li’s criterion for the Riemann hypothesis. J. Number Theory, 77:274–287, 1999. [Boneh 1999] D. Boneh. Twenty years of attacks on the RSA cryptosystem. Notices Amer. Math. Soc., 46:203–213, 1999. [Boneh and Venkatesan 1998] D. Boneh and R. Venkatesan. Breaking RSA may not be equivalent to factoring. In Advances in Cryptology, Proc. Eurocrypt ’98, volume 1514 of Lecture Notes in Computer Science, pages 25–34. Springer–Verlag, 1998. [Borwein 1991] P. Borwein. On the irrationality of (1/(q n + r)). J. Number Theory, 37:253–259, 1991.
REFERENCES 551 [Borwein and Borwein 1987] J. Borwein and P. Borwein. Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity. John Wiley and Sons, 1987. [Borwein et al. 2000] J. Borwein, D. Bradley, and R. Crandall. Computational strategies for the Riemann zeta function. J. Comp. App. Math., 121:247–296, 2000. [Bosma and van der Hulst 1990] W. Bosma and M.-P. van der Hulst. Primality proving with cyclotomy. PhD thesis, University of Amsterdam, 1990. [Bosselaers et al. 1994] A. Bossalaers, R. Govaerts, and J. Vandewalle. Comparison of three modular reduction functions. In D. Stinson, editor, Advances in Cryptology, Proc. Crypto ’93, volume 773 in Lecture Notes in Computer Science, pages 175–186. Springer–Verlag, 1994. [Boyle et al. 1995] P. Boyle, M. Broadie, and P. Glasserman. Monte Carlo methods for security pricing. Unpublished manuscript, June 1995. [Bratley and Fox 1988] P. Bratley and B. Fox. ALGORITHM 659: Implementing Sobol’s quasirandom sequence generator. ACM Trans. Math. Soft., 14:88–100, 1988. [Bredihin 1963] B. Bredihin. Applications of the dispersion method in binary additive problems. Dokl. Akad. Nauk. SSSR, 149:9–11, 1963. [Brent 1979] R. Brent. On the zeros of the Riemann zeta function in the critical strip. Math. Comp., 33:1361–1372, 1979. [Brent 1994] R. Brent. On the period of generalized Fibonacci recurrences. Math. Comp., 63:389–401, 1994. [Brent 1999] R. Brent. Factorization of the tenth Fermat number. Math. Comp., 68:429–451, 1999. [Brent et al. 1993] R. Brent, G. Cohen, and H. te Riele. Improved techniques for lower bounds for odd perfect numbers. Math. Comp., 61:857–868, 1993. [Brent et al. 2000] R. Brent, R. Crandall, K. Dilcher, and C. van Halewyn. Three new factors of Fermat numbers. Math. Comp., 69: 1297–1304, 2000. [Brent and Pollard 1981] R. Brent and J. Pollard. Factorization of the eighth Fermat number. Math. Comp., 36:627–630, 1981. [Bressoud and Wagon 2000] D. Bressoud and S. Wagon. A Course in Computational Number Theory. Key College Publishing, 2000. [Brillhart et al. 1981] J. Brillhart, M. Filaseta, and A. Odlyzko. On an irreducibility theorem of A. Cohn. Canad. J. Math., 33:1055–1059, 1981. [Brillhart et al. 1988] J. Brillhart, D. Lehmer, J. Selfridge, B. Tuckerman, and S. Wagstaff, Jr. Factorizations of b n ± 1, b =2, 3, 5, 6, 7, 10, 11, 12 up to high powers. Second edition, volume 22 of Contemporary Mathematics. Amer. Math. Soc., 1988. [Bruin 2003] N. Bruin. The primitive solutions to x 3 + y 9 = z 2 . http://arxiv.org/find/math/1/au:+Bruin N/0/1/0/all/0/1. J. Number Theory, to appear.
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- Page 556 and 557: 548 REFERENCES [Apostol 1986] T. Ap
- 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 566 and 567: 558 REFERENCES [Goldwasser and Kili
- 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 580 and 581: 572 REFERENCES [Sun and Sun 1992] Z
- Page 582 and 583: 574 REFERENCES [Weisstein 2005] E.
- Page 584 and 585: Index ABC conjecture, 417, 434 abel
- Page 586 and 587: INDEX 579 Catalan problem, ix, 415,
- Page 588 and 589: INDEX 581 discrete arithmetic-geome
- 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
- Page 600 and 601: INDEX 593 Salomaa, A. (with Paun et
- Page 602 and 603: INDEX 595 te Riele, H. (with van de
- Page 604: INDEX 597 Yagle, A., 259, 499, 539
550 REFERENCES<br />
[Bernstein 2004b] D. Bernstein. Factorization myths.<br />
http://cr.yp.to/talks.html#2004.06.14.<br />
[Bernstein 2004c] D. Bernstein. Doubly focused enumeration of locally square<br />
polynomial values. In High primes and misdemeanours: lectures in<br />
honour of the 60th birthday of Hugh Cowie Williams, volume 41 of Fields<br />
Inst. Commun., pages 69–76. Amer. Math. Soc., 2004.<br />
[Bernstein 2004d] D Bernstein. How to find smooth parts of integers.<br />
http://cr.yp.to/papers.html#smoothparts.<br />
[Bernstein 2004e] D. Bernstein. Fast multiplication and its applications. In<br />
J. Buhler and P. Stevenhagen, editors Cornerstones in algorithmic<br />
number theory (tentative title), a Mathematical Sciences Research<br />
Institute Publication. Cambridge University Press, to appear.<br />
[Berrizbeitia 2002] P. Berrizbeitia. Sharpening “PRIMES is in P” for a large<br />
family of numbers.<br />
http://arxiv.org/find/grp math/1/au:+Berrizbeitia/0/1/0/all/0/1.<br />
[Berry 1997] M. Berry. Quantum chaology. Proc. Roy. Soc. London Ser. A,<br />
413:183–198, 1987.<br />
[Berta and Mann 2002] I. Berta and Z. Mann. Implementing elliptic-curve<br />
cryptography on PC and Smart Card. Periodica Polytechnica, Series<br />
Electrical Engineering, 46:47–73, 2002.<br />
[Beukers 2004] F. Beukers. The diophantine equation Ax p + By q = Cz r .<br />
http://www.math.uu.nl/people/beukers/Fermatlectures.pdf.<br />
[Blackburn and Teske 1999] S. Blackburn and E. Teske. Baby-step giant-step<br />
algorithms for non-uniform distributions. Unpublished manuscript, 1999.<br />
[Bleichenbacher 1996] D. Bleichenbacher. Efficiency and security of cryptosystems<br />
based on number theory. PhD thesis, Swiss Federal Institute of<br />
Technology Zürich, 1996.<br />
[Blum et al. 1986] L. Blum, M. Blum, and M. Shub. A simple unpredictable<br />
pseudorandom number generator. SIAM J. Comput., 15:364–383, 1986.<br />
[Bombieri and Iwaniec 1986] E. Bombieri and H. Iwaniec. On the order of<br />
ζ(1/2+it). Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 13:449–472, 1986.<br />
[Bombieri and Lagarias 1999] E. Bombieri and J. Lagarias. Complements to Li’s<br />
criterion for the Riemann hypothesis. J. Number Theory, 77:274–287,<br />
1999.<br />
[Boneh 1999] D. Boneh. Twenty years of attacks on the RSA cryptosystem.<br />
Notices Amer. Math. Soc., 46:203–213, 1999.<br />
[Boneh and Venkatesan 1998] D. Boneh and R. Venkatesan. Breaking RSA may<br />
not be equivalent to factoring. In Advances in Cryptology, Proc.<br />
Eurocrypt ’98, volume 1514 of Lecture Notes in Computer Science, pages<br />
25–34. Springer–Verlag, 1998.<br />
[Borwein 1991] P. Borwein. On the irrationality of (1/(q n + r)). J. Number<br />
Theory, 37:253–259, 1991.