Prime Numbers
Prime Numbers Prime Numbers
572 REFERENCES [Sun and Sun 1992] Z.-H. Sun and Z.-W. Sun. Fibonacci numbers and Fermat’s last theorem. Acta Arith., 60:371–388, 1992. [Swarztrauber 1987] P. Swarztrauber. Multiprocessor FFTs. Parallel Computing, 5:197–210, 1987. [Tanner and Wagstaff 1987] J. Tanner and S. Wagstaff, Jr. New congruences for the Bernoulli numbers. Math. Comp., 48:341–350, 1987. [Tatuzawa 1952] T. Tatuzawa. On a theorem of Siegel. Jap. J. Math., 21:163–178, 1951-1952. [Teitelbaum 1998] J. Teitelbaum. Euclid’s algorithm and the Lanczos method over finite fields. Math. Comp., 67:1665–1678, 1998. [Terr 2000] D. Terr. A modification of Shanks’ baby-step giant-step algorithm. Math. Comp., 69:767–773, 2000. [Teske 1998] E. Teske. Speeding up Pollard’s rho method for computing discrete logarithms. In [Buhler 1998], pages 541–554. [Teske 2001] E. Teske. On random walks for Pollard’s rho method. Math. Comp., 70:809–825, 2001. [Tezuka 1995] S. Tezuka. Uniform Random Numbers: Theory and Practice. Kluwer Academic Publishers, 1995. [Thomas et al. 1986] J. Thomas, J. Keller, and G. Larsen. The calculation of multiplicative inverses over GF (P ) efficiently where P is a Mersenne prime. IEEE Trans. Comp., C-35:478–482, 1986. [Titchmarsh 1986] E. Titchmarsh and D. Heath-Brown. The Theory of the Riemann Zeta-function. Oxford University Press, 1986. [Trevisan and Carvalho 1993] V. Trevisan and J. Carvalho. The composite character of the twenty-second Fermat number. J. Supercomputing, 9:179–182, 1995. [van de Lune et al. 1986] J. van de Lune, H. te Riele, and D. Winter. On the zeros of the Riemann zeta function in the critical strip. IV. Math. Comp., 46:667–681, 1986. [van der Corput 1922] J. van der Corput. Verscharfung der Abschätzungen beim Teilerproblem. Math. Ann., 87:39–65, 1922. [van der Pol 1947] B. van der Pol. An electro-mechanical investigation of the Riemann zeta function in the critical strip. Bull. Amer. Math. Soc., 53, 1947. [Van Loan 1992] C. Van Loan. Computational Frameworks for the Fast Fourier Transform, volume 10 of Frontiers in Applied Mathematics. SIAM, 1992. [van Oorschot and Wiener 1999] P. van Oorschot and M. Wiener. Parallel collision search with cryptanalytic applications. J. Cryptology, 12:1–28, 1999. [van Zyl and Hutchinson] B. van Zyl and D. Hutchinson. Riemann zeros, prime numbers, and fractal potentials. Nonlinear Sciences Abstracts, 2003. http://arxiv.org/abs/nlin.CD/0304038.
REFERENCES 573 [Vaughan 1977] R. Vaughan. Sommes trigonométriques sur les nombres premiers. C. R. Acad. Sci. Paris Sér. A-B, 285:A981–A983, 1977. [Vaughan 1989] R. Vaughan, A new iterative method in Waring’s problem, Acta Arith., 162:1–71, 1989. [Vaughan 1997] R. Vaughan. The Hardy–Littlewood Method. Second edition, volume 125 of Cambridge Tracts in Mathematics. Cambridge University Press, 1997. [Veach 1997] E. Veach. Robust Monte Carlo methods for light transport simulation. PhD thesis, Stanford University, 1997. [Vehka 1979] T. Vehka. Explicit construction of an admissible set for the conjecture that sometimes π(x + y) >π(x)+π(y). Notices Amer. Math. Soc., 26, A-453, 1979. [Vinogradov 1985] I. Vinogradov. Ivan Matveevič Vinogradov: Selected Works. Springer–Verlag, 1985. L. Faddeev, R. Gamkrelidze, A. Karacuba, K. Mardzhanishvili, and E. Miˇsčenko, editors. [Vladimirov et al. 1994] V. Vladimirov, I. Volovich, and E. Zelenov. p-adic Analysis and Mathematical Physics, volume 1 of Series on Soviet and East European Mathematics. World Scientific, 1994. [von zur Gathen and Gerhard 1999] J. von zur Gathen and J. Gerhard. Modern computer algebra. Cambridge University Press, 1999. [Wagstaff 1978] S. Wagstaff, Jr. The irregular primes to 125000. Math. Comp., 32:583–591, 1978. [Wagstaff 1993] S. Wagstaff, Jr. Computing Euclid’s primes. Bull. Inst. Combin. Appl., 8:23–32, 1993. [Wagstaff 2004] S. Wagstaff, Jr. The Cunningham project. http://www.cerias.purdue.edu/homes/ssw/cun/index.html. [Ware 1998] A. Ware. Fast Approximate Fourier Transforms for Irregularly Spaced Data. SIAM Rev., 40:838–856, 1998. [Warren 1995] B. Warren. An interesting group of combination-product sets produces some very nice dissonances. The Journal of the Just Intonation Network, 9(1):1, 4–9, 1995. [Watkins 2004] M. Watkins. Class numbers of imaginary quadratic fields. Math. Comp. 73:907–938, 2004. [Watt 1989] N. Watt. Exponential sums and the Riemann zeta-function. II. J. London Math. Soc., 39, 1989. [Weber 1995] K. Weber. The accelerated GCD algorithm. ACM Trans. Math. Soft., 21:111–122, 1995. [Weber et al. 2005] K. Weber, V. Trevisan, and L. Martins. A modular integer GCD algorithm. Journal of Algorithms, 54:152–167, 2005. [Wedeniwski 2004] S. Wedeniwski. Zetagrid, 2004. http://www.zetagrid.net. [Weiss 1963] E. Weiss. Algebraic Number Theory. McGraw-Hill, 1963.
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- Page 564 and 565: 556 REFERENCES [Dudon 1987] J. Dudo
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- Page 568 and 569: 560 REFERENCES [Joe 1999] S. Joe. A
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- Page 574 and 575: 566 REFERENCES [Oesterlé 1985] J.
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- 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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- Page 604: INDEX 597 Yagle, A., 259, 499, 539
REFERENCES 573<br />
[Vaughan 1977] R. Vaughan. Sommes trigonométriques sur les nombres premiers.<br />
C. R. Acad. Sci. Paris Sér. A-B, 285:A981–A983, 1977.<br />
[Vaughan 1989] R. Vaughan, A new iterative method in Waring’s problem, Acta<br />
Arith., 162:1–71, 1989.<br />
[Vaughan 1997] R. Vaughan. The Hardy–Littlewood Method. Second edition,<br />
volume 125 of Cambridge Tracts in Mathematics. Cambridge University<br />
Press, 1997.<br />
[Veach 1997] E. Veach. Robust Monte Carlo methods for light transport simulation.<br />
PhD thesis, Stanford University, 1997.<br />
[Vehka 1979] T. Vehka. Explicit construction of an admissible set for the<br />
conjecture that sometimes π(x + y) >π(x)+π(y). Notices Amer. Math.<br />
Soc., 26, A-453, 1979.<br />
[Vinogradov 1985] I. Vinogradov. Ivan Matveevič Vinogradov: Selected Works.<br />
Springer–Verlag, 1985. L. Faddeev, R. Gamkrelidze, A. Karacuba, K.<br />
Mardzhanishvili, and E. Miˇsčenko, editors.<br />
[Vladimirov et al. 1994] V. Vladimirov, I. Volovich, and E. Zelenov. p-adic<br />
Analysis and Mathematical Physics, volume 1 of Series on Soviet and<br />
East European Mathematics. World Scientific, 1994.<br />
[von zur Gathen and Gerhard 1999] J. von zur Gathen and J. Gerhard. Modern<br />
computer algebra. Cambridge University Press, 1999.<br />
[Wagstaff 1978] S. Wagstaff, Jr. The irregular primes to 125000. Math. Comp.,<br />
32:583–591, 1978.<br />
[Wagstaff 1993] S. Wagstaff, Jr. Computing Euclid’s primes. Bull. Inst. Combin.<br />
Appl., 8:23–32, 1993.<br />
[Wagstaff 2004] S. Wagstaff, Jr. The Cunningham project.<br />
http://www.cerias.purdue.edu/homes/ssw/cun/index.html.<br />
[Ware 1998] A. Ware. Fast Approximate Fourier Transforms for Irregularly Spaced<br />
Data. SIAM Rev., 40:838–856, 1998.<br />
[Warren 1995] B. Warren. An interesting group of combination-product sets<br />
produces some very nice dissonances. The Journal of the Just Intonation<br />
Network, 9(1):1, 4–9, 1995.<br />
[Watkins 2004] M. Watkins. Class numbers of imaginary quadratic fields. Math.<br />
Comp. 73:907–938, 2004.<br />
[Watt 1989] N. Watt. Exponential sums and the Riemann zeta-function. II. J.<br />
London Math. Soc., 39, 1989.<br />
[Weber 1995] K. Weber. The accelerated GCD algorithm. ACM Trans. Math.<br />
Soft., 21:111–122, 1995.<br />
[Weber et al. 2005] K. Weber, V. Trevisan, and L. Martins. A modular integer<br />
GCD algorithm. Journal of Algorithms, 54:152–167, 2005.<br />
[Wedeniwski 2004] S. Wedeniwski. Zetagrid, 2004. http://www.zetagrid.net.<br />
[Weiss 1963] E. Weiss. Algebraic Number Theory. McGraw-Hill, 1963.
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