@inproceedings{Chudnovsky&Chudnovsky:1989,
	key = "Chudnovsky and Chudnovsky 1989",
	author = "D. V. Chudnovsky and G. V. Chudnovsky",
	title = "Use of computer algebra for diophantine and differential
equations",
	booktitle = "Computer Algebra",
	year = 1989,
	publisher = MD,
	pages = "1-81"}

@article{Frumkin:1982,
	key = "Frumkin 1982",
	author = "M. A. Frumkin",
	title = "Complexity questions in number theory",
	journal = "Zapiski Nauchn. Semin. Leningr. Otdel. Matem. Inst. Acad. Sci. USSR",
	volume = 118,
	year = 1982,
	pages = "188-210",
	note = "English translation in {\it J. Soviet Math.} {\bf 29} (1985), 1502--1517"}

@article{Collins&Musser:1977,
	key = "G. Collins and Musser 1977",
	author = "G. E. Collins and D. R. Musser",
	title = "Analysis of the {Pope-Stein} division algorithm",
	journal = IPL,
	volume = 6,
	year = 1977,
	pages = "151-155"}

@article{Collins:1973,
	key = "G. Collins 1973",
	author = "G. E. Collins",
	title = "Computer algebra of polynomials and rational functions",
	journal = AMM,
	volume = 80,
	year = 1973,
	pages = "725-755"}

@article{Chalk&Williams:1965,
	key = "Chalk and Williams 1965",
	author = "J. H. H. Chalk and K. S. Williams",
	title = "The distribution of solutions of congruences",
	journal = "Mathematika",
	volume = 12,
	year = 1965,
	pages = "176-192"}

@article{Bateman:1972,
	key = "Bateman 1972",
	author = "P. T. Bateman",
	title = "The distribution of values of the {Euler} function",
	journal = AA,
	volume = 21,
	year = 1972,
	pages = "329-345"}

@article{Brent:1976b,
	key = "Brent 1976b",
	author = "R. P. Brent",
	title = "Fast multiple-precision evaluation of elementary
functions",
	journal = JACM,
	volume = 23,
	year = "{\noopsort 1976b}1976",
	pages = "242-251"}

@techreport{Johnson:1974,
	key = "S. Johnson 1974",
	author = "S. M. Johnson",
	title = "Certain number-theoretic questions in access control",
	institution = "RAND Corporation",
	number = "R-1494-NSF",
	month = "January",
	year = 1974}

@article{von.zur.Gathen:1987a,
	key = "von zur Gathen 1987a",
	author = "Gathen, J. von zur",
	title = "Factoring polynomials and primitive elements for special
primes",
	journal = TCS,
	volume = 52,
	year = "{\noopsort{1987a}}1987",
	pages = "77-89"}

@article{Hooley:1964,
	key = "Hooley 1964",
	author = "C. J. Hooley",
	title = "On the distribution of the roots of polynomial congruences",
	journal = "Mathematika",
	volume = 11,
	year = 1964,
	pages = "39-49"}

@article{Lehmer:1972,
	key = "D. H. Lehmer 1972",
	author = "D. H. Lehmer",
	title = "On reciprocally weighted partitions",
	journal = AA,
	volume = 21,
	year = 1972,
	pages = "379-388"}

@article{Williams:1969,
	key = "K. Williams 1969",
	author = "K. S. Williams",
	title = "Polynomials with irreducible factors of specified degree",
	journal = CMB,
	volume = 12,
	year = 1969,
	pages = "221-223"}

@article{Wyman:1972,
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	author = "B. F. Wyman",
	title = "What is a reciprocity law?",
	journal = AMM,
	volume = 79,
	year = 1972,
	pages = "571-586",
	note = "Corrigendum: {\bf 80} (1973), 281"}

@article{Lenstra&Lenstra&Lovasz:1982,
	key = "A. K. Lenstra, Lenstra, and {Lov\'asz} 1982",
	author = "A. K. Lenstra and Lenstra, Jr., H. W. and L. {Lov\'asz}",
	title = "Factoring polynomials with rational coefficients",
	journal = MA,
	volume = 261,
	year = 1982,
	pages = "515-534"}

@book{Borevich&Shafarevich:1966,
	key = "Borevich and Shafarevich 1966",
	author = "Z. I. Borevich and I. R. Shafarevich",
	title = "Number theory",
	series = "Pure and Applied Mathematics",
	volume = 20,
	year = 1966,
	publisher = AP,
	address = NY}

@book{Cassels&Frohlich:1967,
	key = "Cassels and {Fr\"ohlich} 1967",
	editor = "J. W. S. Cassels and A. {Fr\"ohlich}",
	title = "Algebraic Number Theory",
	publisher = "Thompson Book Co.",
	year = 1967,
	address = "Washington",
	note = "Reprinted by Academic Press, 1986"}

@book{Hasse:1980,
	key = "Hasse 1980",
	author = "H. Hasse",
	title = "Number Theory",
	publisher = SV,
	series = "Grundlehren der mathematischen Wissenschaften in
Einzeldarstellungen",
	volume = 229,
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	address = "Berlin"}

@book{Lang:1986,
	key = "Lang 1986",
	author = "S. Lang",
	title = "Algebraic Number Theory",
	publisher = SV,
	address = NY,
	year = 1986}

@book{Marcus:1977,
	key = "Marcus 1977",
	author = "D. A. Marcus",
	title = "Number Fields",
	publisher = SV,
	address = NY,
	year = 1977}

@book{Washington:1982,
	key = "Washington 1982",
	author = "L. C. Washington",
	title = "Introduction to Cyclotomic Fields",
	publisher = SV,
	address = NY,
	year = 1982}

@article{Beynon&Iliopoulos:1985,
	key = "Beynon and Iliopoulos 1985",
	author = "W. M. Beynon and C. S. Iliopoulos",
	title = "Computing a basis for a finite abelian $p$-group",
	journal = IPL,
	volume = 20,
	year = 1985,
	pages = "161-163"}

@article{Hornfeck&Wirsing:1957,
	key = "Hornfeck and Wirsing 1957",
	author = "B. Hornfeck and E. Wirsing",
	title = "{\"Uber} die {H\"aufigkeit} vollkommener {Zahlen}",
	journal = MA,
	volume = 133,
	year = 1957,
	pages = "431-438"}

@book{Koblitz:1977,
	key = "Koblitz 1977",
	author = "N. Koblitz",
	title = "$p$-adic Numbers, $p$-adic Analysis, and Zeta-Functions",
	publisher = SV,
	address = NY,
	year = 1977}

@article{McCullagh:1981,
	key = "McCullagh 1981",
	author = "P. McCullagh",
	title = "A rapidly convergent series for computing $\psi(z)$ and
its derivatives",
	journal = MC,
	volume = 36,
	year = 1981,
	pages = "247-248"}

@article{Netto:1884,
	key = "Netto 1884",
	author = "E. Netto",
	title = "{\"Uber} die {Factorenzerlegung} der {Discriminanten}
algebraischer {Gleichungen}",
	journal = MA,
	volume = 24,
	year = 1884,
	pages = "579-587"}

@article{von.Neumann:1951,
	key = "von Neumann 1951",
	author = "Neumann, J. von",
	title = "Various techniques used in connection with random
		 digits",
	journal = JRNBS,
	volume = 3,
	year = 1951,
	pages = "36-38",
	note = "Reprinted in {\it Collected Works,} Vol.~V, pp.~768--770"
	}

@article{Pollard:1976,
	key = "Pollard 1976",
	author = "J. M. Pollard",
	title = "Implementation of number-theoretic transforms",
	journal = ELETT,
	volume = 12,
	year = 1976,
	pages = "378-379"}

@article{Perelli&Zannier:1982,
	key = "Perelli and Zannier 1982",
	author = "A. Perelli and U. Zannier",
	title = "On periodic mod $p$ sequences",
	journal = JNT,
	volume = 15,
	year = 1982,
	pages = "77-82"}

@book{Polya&Szego:1972,
	key = "{P\'olya} and {Szeg\"o} 1972",
	author = "G. {P\'olya} and G. {Szeg\"o}",
	title = "Problems and Theorems in Analysis, I",
	publisher = SV,
	address = "Berlin",
	year = 1972}

@book{Rabiner&Gold:1975,
	key = "Rabiner and Gold 1975",
	author = "L. R. Rabiner and B. Gold",
	title = "Theory and Application of Digital Signal Processing",
	publisher = PH,
	address = "Englewood Cliffs, N. J.",
	year = 1975}

@book{Rogers:1967,
	key = "Rogers 1967",
	author = "Rogers, Jr., H.",
	title = "Theory of Recursive Functions and Effective Computability",
	publisher = MH,
	address = NY,
	year = 1967,
	note = "Reprinted by MIT Press, 1987"}

@book{Strang:1988,
	key = "Strang 1988",
	author = "G. Strang",
	title = "Linear Algebra and its Applications",
	publisher = HBJ,
	address = "San Diego",
	year = 1988}

@article{Taylor:1981,
	key = "Taylor 1981",
	author = "F. J. Taylor",
	title = "Large moduli multipliers for signal processing",
	journal = IEEE-TCS,
	volume = 28,
	year = 1981,
	pages = "731-736"}

@book{Titchmarsh:1975,
	key = "Titchmarsh 1975",
	author = "E. C. Titchmarsh",
	title = "The Theory of Functions",
	publisher = OUP,
	address = "London",
	year = 1975}

@article{Buell&Ward:1989,
	key = "Buell and Ward 1989",
	author = "D. A. Buell and R. L. Ward",
	title = "A multiprecise integer arithmetic package",
	journal = "J. Supercomputing",
	volume = 3,
	year = 1989,
	pages = "89-107"}

@phdthesis{Sorenson:1991b,
	key = "Sorenson 1991b",
	author = "J. Sorenson",
	title = "Algorithms in number theory",
	school = "University of Wisconsin -- Madison",
	year = "{\noopsort{1991b}}1991",
	month = "June",
	note = "Computer Sciences Department Technical Report \#1027"}

@techreport{Kung:1973,
	key = "Kung 1973",
	author = "H. T. Kung",
	title = "Fast evaluation and interpolation",
	institution = "Carnegie Mellon University",
	month = "January",
	year = 1973}

@inproceedings{Shoup&Smolensky:1991,
	key = "Shoup and Smolensky 1991",
	author = "V. Shoup and R. Smolensky",
	title = "Lower bounds for polynomial evaluation and 
		 interpolation problems",
	year = 1991,
	booktitle = FOCS91,
	pages = "378-383"}

@article{Bachmann:1912,
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	title = "Eine zahlentheoretische {B}emerkung",
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	year = 1912,
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@incollection{Schonhage:1991,
	key = "{Sch\"onhage} 1991",
	author = "A. {Sch\"onhage}",
	title = "Fast reduction and composition of binary quadratic forms",
	booktitle = ISSAC91,
	editor = "S. M. Watt",
	publisher = "ACM Press",
	year = 1991,
	pages = "128-133"}

@incollection{Flajolet&Odlyzko:1990,
	key = "Flajolet and Odlyzko 1990",
	author = "P. Flajolet and A. Odlyzko",
	title = "Random mapping statistics",
	booktitle = EUROCRYPT89,
	editor = "J.-J. Quisquater and J. Vandewalle",
	year = 1990,
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	pages = "329-354"}

@book{Cormen&Leiserson&Rivest:1990,
	key = "Cormen, Leiserson, and Rivest 1990",
	author = "T. H. Cormen and C. E. Leiserson and R. L. Rivest",
	title = "Introduction to Algorithms",
	publisher = MIT,
	year = 1990}

@book{Pohst&Zassenhaus:1989,
	key = "Pohst and Zassenhaus 1989",
	author = "M. Pohst and H. Zassenhaus",
	title = "Algorithmic Algebraic Number Theory",
	publisher = CUP,
	year = 1989}

@article{Peralta:1992,
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	author = "R. C. Peralta",
	title = "On the distribution of quadratic residues and nonresidues
modulo a prime number",
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	volume = 58,
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	pages = "443-440"}

@article{Eichenauer:1991,
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	author = "J. Eichenauer-Herrmann",
	title = "Inversive congruential pseudorandom numbers avoid the planes",
	journal = MC,
	volume = 56,
	year = 1991,
	pages = "297-301"}

@article{MillerW:1987,
	key = "W. Miller 1987",
	author = "W. Miller",
	title = "The maximum order of an element of a finite symmetric group",
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	year = 1987,
	pages = "497-506"}

@book{Barlow:1811,
	key = "Barlow 1811",
	author = "P. Barlow",
	title = "An Elementary Investigation of the Theory of Numbers, With its Application
to the Indeterminate and Diophantine Analysis, the Analytical and Geometrical Division of the
Circle, and Several Other Curious Algebraical and Arithmetical Problems",
	publisher = "J. Johnson and Co.",
	address = "London",
	year = 1811}

@inproceedings{Cai&Lipton&Zalcstein:1994,
	key = "Cai, Lipton, and Zalcstein 1994",
	author = "J.-Y. Cai and R. J. Lipton and Y. Zalcstein",
	title = "The complexity of the membership problem for
$2$-generated commutative semigroups of rational matrices",
	booktitle = FOCS94,
	year = 1994,
	pages = "135-142"}

@inproceedings{Cai&Fuchs&Kozen&Liu:1994,
	key = "Cai, Fuchs, Kozen, and Liu 1994",
	author = "J.-Y. Cai and W. H. Fuchs and D. Kozen and Z. Liu",
	title = "Efficient average-case algorithms for the modular group",
	booktitle = FOCS94,
	year = 1994,
	pages = "143-152"}

@article{Filaseta&Robinson&Wheeler:1994,
	key = "Filaseta, Robinson, and Wheeler 1994",
	author = "M. Filaseta and M. L. Robinson and F. S. Wheeler",
	title = "The minimal {Euclidean} norm of an algebraic number is
effectively computable",
	journal = JA,
	volume = 16,
	year = 1994,
	pages = "309-333"}

@article{Gladwin:1964,
	key = "Gladwin 1964",
	author = "H. T. Gladwin",
	title = "An algorithm for converting integers from base
		 $\alpha$ to base $\beta$",
	journal = CACM,
	volume = 7,
	year = 1964,
	pages = "241-242"}

@article{Jebelean:1993d,
	key = "Jebelean 1993d",
	author = "T. Jebelean",
	title = "An algorithm for exact division",
	journal = JSC,
	volume = 15,
	year = "{\noopsort 1993d}1993",
	pages = "169-180"}

@article{Sasaki&Sasaki:1992,
	key = "Sasaki and Sasaki 1992",
	author = "T. Sasaki and M. Sasaki",
	title = "On integer-to-rational conversion algorithm",
	journal = ASB,
	volume = 26,
	year = 1992,
	pages = "19-21"}

@incollection{Fellows&Koblitz:1993,
	key = "Fellows and Koblitz 1993",
	author = "M. R. Fellows and N. Koblitz",
	title = "Fixed-parameter complexity and cryptography",
	booktitle = AAECC10,
	series = LNICS,
	volume = 673,
	year = 1993,
	editor = "G. Cohen and T. Mora and O. Moreno",
	pages = "121-131",
	publisher = SV}

@incollection{Pohst:1992,
	key = "Pohst 1992",
	author = "M. Pohst",
	title = "Some aspects of computational algebraic number theory",
	booktitle = "Proc. Int'l. Conf. on Algebra",
	series = "Contemporary Mathematics",
	volume = "131 (Part 3)",
	editor = "L. A. Bokut' and Yu L. Ershov and A. I. Kostrikin",
	publisher = AMS,
	year = 1992,
	pages = "461-474"}