References

AbbottBronsteinMulders1999

Fast deterministic computation of determinants of dense matrices ACM International Symposium on Symbolic and Algebraic Computation 1999

Apostol1997

Apostol, Tom : Modular functions and Dirichlet series in number theory, Springer (1997)

ArnoldMonagan2011

Arnold, Andrew and Monagan, Michael : Calculating cyclotomic polynomials, Mathematics of Computation 80:276 (2011) 2359–2379

BaiWag1980

Robert Baillie; Samuel S. Wagstaff, Jr. (October 1980). “Lucas Pseudoprimes”. Mathematics of Computation. 35 (152): 1391–1417.

BerTas2010
  1. Berend and T. Tassa : Improved bounds on Bell numbers and on moments of sums of random variables, Probability and Mathematical Statistics vol. 30 (2010) 185–205

Bodrato2010

Bodrato, Marco A Strassen-like Matrix Multiplication Suited for Squaring and Higher Power Computation. Proceedings of the ISSAC 2010 München, Germany, 25-28 July, 2010

BrentKung1978

Brent, R. P. and Kung, H. T. : Fast Algorithms for Manipulating Formal Power Series, J. ACM 25:4 (1978) 581–595

BuhlerCrandallSompolski1992

Buhler, J.P. and Crandall, R.E. and Sompolski, R.W. : Irregular primes to one million : Math. Comp. 59:2000 (1992) 717–722

Chen2003

Zhuo Chen and John Greene : Some Comments on {Baillie–PSW} Pseudoprimes, The Fibonacci Quaterly 41:4 (2003) 334–344

Coh1996

Cohen, Henri : A course in computational algebraic number theory, Springer, 1996

Col1971

Collins, George E. : The Calculation of Multivariate Polynomial Resultants, SYMSAC ‘71, ACM 1971 212–222

CraPom2005

Richard Crandall and Carl Pomerance: Prime numbers: a computational perspective. 2005.

DelegliseNicolasZimmermann2009

Deleglise, Marc and Niclas, Jean-Louis and Zimmermann, Paul : Landau’s function for one million billions, J. Th'eor. Nombres Bordeaux 20:3 (2009) 625–671

DomKanTro1987

Domich, P. D. and Kannan, R. and Trotter, L. E. Jr. : Hermite Normal Form Computation Using Modulo Determinant Arithmetic, Math. Operations Res. (12) 1987 50-59

Dus1999
  1. Dusart, “The kth prime is greater than k(ln k+ln ln k-1) for k> 2,” Math. Comp., 68:225 (January 1999) 411–415.

FieHof2014

Fieker C. and Hofmann T.: “Computing in quotients of rings of integers” LMS Journal of Computation and Mathematics, 17(A), 349-365

GraMol2010

Torbjorn Granlund and Niels Moller : Improved Division by Invariant Integers https://gmplib.org/~tege/division-paper.pdf

GowWag2008

Jason Gower and Sam Wagstaff : “Square form factoring” Math. Comp. 77, 2008, pp 551-588, https://doi.org/10.1090/S0025-5718-07-02010-8

HanZim2004

Guillaume Hanrot and Paul Zimmermann : Newton Iteration Revisited (2004) https://www.loria.fr/~zimmerma/papers/fastnewton.ps.gz

Har2012

Hart, William B.. (2012) A one line factoring algorithm. Journal of the Australian Mathematical Society, Volume 92 (Number 1). pp. 61-69.

Iliopoulos1989

Iliopoulos, C. S., Worst-Case Complexity Bounds on Algorithms for Computing the Canonical Structure of Finite Abelian Groups and the Hermite and Smith Normal Forms of an Integer Matrix : SIAM J. Computation 18:4 (1989) 658

KanBac1979

Kannan, R. and Bachem, A. : Polynomial algorithms for computing and the Smith and Hermite normal forms of an integer matrix, SIAM J. Computation vol. 9 (1979) 499–507

Kahan1991

Kahan, William: Computing a Real Cube Root. https://csclub.uwaterloo.ca/~pbarfuss/qbrt.pdf

LukPatWil1996
    1. Lukes and C. D. Patterson and H. C. Williams “Some results on pseudosquares” Math. Comp. 1996, no. 65, 361–372

MasRob1996
  1. Massias and G. Robin, “Bornes effectives pour certaines fonctions concernant les nombres premiers,” J. Theorie Nombres Bordeaux, 8 (1996) 215-242.

NakTurWil1997

Nakos, George and Turner, Peter and Williams, Robert : Fraction-free algorithms for linear and polynomial equations, ACM SIGSAM Bull. 31 (1997) 3 11–19

Mul2000

Thom Mulders : On Short Multiplications and Divisions, AAECC vol. 11 (2000) 69–88

Paterson1973

Michael S. Paterson and Larry J. Stockmeyer : On the number of nonscalar multiplications necessary to evaluate polynomials, SIAM Journal on Computing (1973)

PernetStein2010

Pernet, C. and Stein, W. : Fast computation of Hermite normal forms of random integer matrices ,J. Number Theory 130:17 (2010) 1675–1683

Rademacher1937

Rademacher, Hans : On the partition function \(p(n)\) Proc. London Math. Soc vol. 43 (1937) 241–254

RosSch1962

Rosser, J. Barkley; Schoenfeld, Lowell: Approximate formulas for some functions of prime numbers. Illinois J. Math. 6 (1962), no. 1, 64–94.

SorWeb2016

Sorenson, Jonathan and Webster, Jonathan : Strong pseudoprimes to twelve prime bases. Math. Comp. 86 (2017), 985-1003, https://doi.org/10.1090/mcom/3134

Stehle2010

Stehl'e, Damien : Floating-Point LLL: Theoretical and Practical Aspects, in Nguyen, Phong Q. and Vall'ee, Brigitte : The LLL Algorithm: Survey and Applications (2010) 179–213

Stein2007

Stein, William A.: Modular forms, a computational approach. American Mathematical Society. 2007

StoMul1998

Storjohann, Arne and Mulders, Thom : Fast algorithms for linear algebra modulo \(N\) : Algorithms—{ESA} ‘98 (Venice), Lecture Notes in Comput. Sci. 1461 139–150

ThullYap1990

Thull, K. and Yap, C. : A Unified Approach to {HGCD} Algorithms for Polynomials and Integers, (1990)

Villard2007

Villard, Gilles : Certification of the QR Factor R and of Lattice Basis Reducedness, In proceedings of ACM International Symposium on Symbolic and Algebraic Computation (2007) 361–368 ACM Press.

WaktinsZeitlin1993

Watkins, W. and Zeitlin, J. : The minimal polynomial of $cos(2pi/n)$ The American Mathematical Monthly 100:5 (1993) 471–474

Whiteman1956

Whiteman, A. L. : A sum connected with the series for the partition function, Pacific Journal of Mathematics 6:1 (1956) 159–176