Reference Database
(references for the Prime Pages)
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This is the Prime Pages' interface to our BibTeX database.  Rather than being an exhaustive database, it just lists the references we cite on these pages.  Please let me know of any errors you notice.
References: [ Home | Author index | Key index | Search ]

All items with keys beginning with the letter(s): a

Akushskii, I. Ya. and Burtsev, V. M., "Realization of primality tests for Mersenne and Fermat numbers," Vestnik Akad. Nauk Kazakh. SSR,:1 (1986) 52--59.  MR 843070
M. Agrawal and S. Biswas, Primality and identity testing via Chinese remaindering.  In "40th Annual Symposium on Foundations of Computer Science (New York, 1999)," IEEE Computer Soc., Los Alamitos, CA, 1999.  pp. 202--208, MR1917560
S. Ahlgren and M. Boylan, "Arithmetic properties of the partition function," Invent. Math., 153:3 (2003) 487--502.  MR2000466
A. O.L. Atkin and D. J. Bernstein, "Prime sieves using binary quadratic forms," Math. Comp., 73:246 (2004) 1023--1030 (electronic).  MR2031423
L. M. Adleman, On distinguishing prime numbers from composite numbers.  In "Proc. 21st Ann. Symp. Found. Comput. Sci.," 1980.  pp. 387--406,
T. Agoh, K. Dilcher and L. Skula, "Wilson quotients for composite moduli," Math. Comp., 67 (1998) 843--861.  MR 98h:11003 (Abstract available)
I. O. Angell and H. J. Godwin, "Some factorizations of 10n± 1," Math. Comp., 28 (1974) 307--308.  MR 48:8366
I. O. Angell and H. J. Godwin, "On truncatable primes," Math. Comp., 31 (1977) 265--267.  MR 55:248
Agoh, Takashi, "On Sophie Germain primes," Tatra Mt. Math. Publ., 20 (2000) 65--73.  Number theory (Liptovský Ján, 1999).  MR 1845446
W. R. Alford, A. Granville and C. Pomerance, "There are infinitely many Carmichael numbers," Ann. of Math. (2), 139 (1994) 703--722.  MR 95k:11114
W. R. Alford, A. Granville and C. Pomerance, On the difficulty of finding reliable witnesses.  In "Algorithmic Number Theory, First International Symposium, ANTS-I," L. M. Adleman and M. D. Huang editors, Lecture Notes in Computer Science Vol, 877, Springer-Verlag, 1994.  Berlin, pp. 1--16, MR 96d:11136
L. M. Adlemann and M. D. Huang, Primality testing and two dimensional Abelian varieties over finite fields., Lecture Notes in Mathematics Vol, 1512, Springer-Verlag, 1992.  Berlin, pp. viii+142, ISBN 3-540-55308-8. MR 93g:11128
S. Ahlgren, "Distribution of the partition function modulo composite integers M," Math. Ann., 318:4 (2000) 795--803.  MR1802511
R. André-Jeannin, "On the existence of even Fibonacci pseudoprimes with parameters P and Q," Fibonacci Quart., 34:1 (1996) 75--78.  MR 96m:11013
M. Agrawal, N. Kayal and N. Saxena, "PRIMES in P," Ann. of Math. (2), 160:2 (2004) 781--793.  Available from
Abstract: We present a deterministic polynomial-time algorithm that determines whether an input number n is prime or composite.
L. M. Adleman and F. T. Leighton, "An O(n1/10.89) primality testing algorithm," Math. Comp., 36:153 (1981) 261--266.  MR 82c:10009
A. O. L. Atkin and R. G. Larson, "On a primality test of Solovay and Strassen," SIAM J. Comput., 11:4 (1982) 789--791.  MR 84d:10013
W. W. Adams, E. Liverance and D. Shanks, "Infinitely many necessary and sufficient conditions for primality," Bull. Inst. Combin. Appl., 3 (1991) 69--76.  MR 93e:11011
A. O. L. Atkin and F. Morain, "Elliptic curves and primality proving," Math. Comp., 61:203 (July 1993) 29--68.  MR 93m:11136
T. M. Apostol, Introduction to analytic number theory, Springer-Verlag, New York, NY, 1976.  pp. xii+338, ISBN 0-387-90163-9. MR 55:7892 [QA241.A6]
L. M. Adleman, C. Pomerance and R. S. Rumely, "On distinguishing prime numbers from composite numbers," Ann. Math., 117:1 (1983) 173--206.  MR 84e:10008 [The first of the modern primality tests.]
R. C. Archibald, "Remarks on Klien's `Famous problems of elementary geometry'," Amer. Math. Monthly, 21 (1914) 247--259.
R. C. Archibald, "Mersenne's numbers," Scripta Math., 3 (1935) 112--119.
F. Arnault, "Rabin-Miller primality test: composite numbers which pass it," Math. Comp., 64:209 (1995) 355--361.  MR 95c:11152
F. Arnault, "The Rabin-Monier theorem for Lucas pseudoprimes," Math. Comp., 66:218 (1997) 869--881.  MR 97f:11009
Abstract: We give bounds on the number of pairs (p,q) with 0< p,q< n such that a composite number n is a strong Lucas pseudoprime with respect to the parameters (p,q).
P. Arrioti, "Bonaventura cavalieri, marin mersenne, and the reflecting telescope," Isis, 66 (1997) 303--321.
M. Abramowitz and I. Stegun editors, Handbook of mathematical functions--with formulas, graphs, and mathematical tables, Dover Pub., 1974.  New York, NY, pp. xiv+1046, ISBN 0-486-61272-4. MR 94b:00012
W. W. Adams and D. Shanks, "Strong primality tests that are not sufficient," Math. Comp., 39:159 (1982) 255--300.  MR 84c:10007
A. O. L. Atkin, "Lecture notes of a conference," Boulder Colorado, (August 1986) Manuscript. [See also [AM93].]
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