M. Agrawal, N. Kayal, and N. Saxena, PRIMES is in P, Annals of Mathematics, vol.160, issue.2, pp.781-793, 2004.
DOI : 10.4007/annals.2004.160.781

A. V. Aho, J. E. Hopcroft, and J. D. Ullman, The design and analysis of computer algorithms, 1974.

L. I. Bluestein, A linear filtering approach to the computation of discrete Fourier transform, IEEE Transactions on Audio and Electroacoustics, vol.18, issue.4, pp.451-455, 1970.
DOI : 10.1109/TAU.1970.1162132

A. Bostan, P. Gaudry, and É. Schost, Linear Recurrences with Polynomial Coefficients and Application to Integer Factorization and Cartier???Manin Operator, SIAM Journal on Computing, vol.36, issue.6, pp.1777-1806, 2007.
DOI : 10.1137/S0097539704443793

URL : https://hal.archives-ouvertes.fr/inria-00103401

C. B. Boyer, A History of Mathematics., Biometrics, vol.49, issue.2, 1985.
DOI : 10.2307/2532593

R. P. Brent, Fast Multiple-Precision Evaluation of Elementary Functions, Journal of the ACM, vol.23, issue.2, pp.242-251, 1976.
DOI : 10.1145/321941.321944

R. P. Brent and P. Zimmermann, Modern Computer Arithmetic, 2010.
DOI : 10.1017/CBO9780511921698

URL : https://hal.archives-ouvertes.fr/cel-01500109

P. Bürgisser, M. Clausen, and M. A. Shokrollahi, Algebraic complexity theory, 1997.
DOI : 10.1007/978-3-662-03338-8

S. A. Cook, On the minimum computation time of functions, Transactions of the American Mathematical Society, vol.142, 1966.
DOI : 10.1090/S0002-9947-1969-0249212-8

J. W. Cooley and J. W. Tukey, An algorithm for the machine calculation of complex Fourier series, Mathematics of Computation, vol.19, issue.90, pp.297-301, 1965.
DOI : 10.1090/S0025-5718-1965-0178586-1

R. Crandall and B. Fagin, Discrete weighted transforms and large-integer arithmetic, Mathematics of Computation, vol.62, issue.205, pp.305-324, 1994.
DOI : 10.1090/S0025-5718-1994-1185244-1

R. Crandall and C. Pomerance, Prime numbers. A computational perspective, 2005.

R. Creutzburg and M. Tasche, Parameter determination for complex number-theoretic transforms using cyclotomic polynomials, Mathematics of Computation, vol.52, issue.185, pp.189-200, 1989.
DOI : 10.1090/S0025-5718-1989-0946602-9

A. De, P. P. Kurur, C. Saha, and R. Saptharishi, Fast Integer Multiplication Using Modular Arithmetic, SIAM Journal on Computing, vol.42, issue.2, pp.685-699, 2013.
DOI : 10.1137/100811167

URL : http://arxiv.org/abs/0801.1416

J. Écalle, Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac. Hermann, collection: Actualités mathématiques, 1992.

M. Fürer, On the complexity of integer multiplication (extended abstract), 1989.

M. Fürer, Faster integer multiplication, Proceedings of the Thirty-Ninth ACM Symposium on Theory of Computing, STOC 2007, pp.57-66, 2007.

M. Fürer, Faster Integer Multiplication, SIAM Journal on Computing, vol.39, issue.3, pp.979-1005, 2009.
DOI : 10.1137/070711761

M. Fürer, How Fast Can We Multiply Large Integers on an Actual Computer?, 2014.
DOI : 10.1007/978-3-642-54423-1_57

J. Zur-gathen and J. Gerhard, Modern Computer Algebra, 2002.
DOI : 10.1017/CBO9781139856065

F. Q. Gouvêa, p-adic numbers. An introduction. Universitext, 1993.

T. Granlund, GMP, the GNU multiple precision arithmetic library, 1991.

D. Harvey, J. Van-der-hoeven, and G. Lecerf, Faster Polynomial Multiplication over Finite Fields, Journal of the ACM, vol.63, issue.6
DOI : 10.1145/3005344

URL : https://hal.archives-ouvertes.fr/hal-01022757

D. R. Heath-brown, Almost-primes in arithmetic progressions and short intervals, Mathematical Proceedings of the Cambridge Philosophical Society, vol.28, issue.03, pp.357-375, 1978.
DOI : 10.1112/jlms/s2-8.1.73

D. R. Heath-brown, Zero-Free Regions for Dirichlet L-Functions, and the Least Prime in an Arithmetic Progression, Proc. London Math. Soc. (3), pp.265-338, 1992.
DOI : 10.1112/plms/s3-64.2.265

M. T. Heideman, D. H. Johnson, and C. S. Burrus, Gauss and the history of the fast Fourier transform, Archive for History of Exact Sciences, vol.4, issue.3, pp.265-277, 1985.
DOI : 10.1007/BF00348431

A. Karatsuba and J. Ofman, Óìíîaeåíèå ìíîãîçíàoeíûõ oeèñåë íà àâòîìàòàõ. Doklady Akad, Nauk SSSR, vol.7, pp.293-294, 1962.

A. Karatsuba and J. Ofman, Multiplication of multidigit numbers on automata, Soviet Physics Doklady, vol.7, pp.595-596, 1963.

D. E. Knuth, The Art of Computer Programming, 1969.

D. E. Knuth, The art of computer programming Sorting and Searching, 1998.

Y. V. Linnik, On the least prime in an arithmetic progression I. The basic theorem, Rec. Math. (Mat. Sbornik) N.S, vol.15, issue.57, pp.139-178, 1944.

Y. V. Linnik, On the least prime in an arithmetic progression II. The Deuring-Heilbronn phenomenon, Rec. Math. (Mat. Sbornik) N.S, vol.15, issue.57, pp.347-168, 1944.

R. E. Moore, Interval Analysis, N.J, 1966.

O. Neugebauer, The Exact Sciences in Antiquity, 1957.

C. H. Papadimitriou, Computational Complexity, 1994.

J. M. Pollard, The fast Fourier transform in a finite field, Mathematics of Computation, vol.25, issue.114, pp.365-374, 1971.
DOI : 10.1090/S0025-5718-1971-0301966-0

C. Pomerance, Recent developments in primality testing, The Mathematical Intelligencer, vol.31, issue.21, pp.97-10581, 1980.
DOI : 10.1007/BF03022861

C. M. Rader, Discrete Fourier transforms when the number of data samples is prime, Proc. IEEE, pp.1107-1108, 1968.
DOI : 10.1109/PROC.1968.6477

K. R. Rao, D. N. Kim, and J. J. Hwang, Fast Fourier Transform -Algorithms and Applications. Signals and Communication Technology, 2010.
DOI : 10.1007/978-1-4020-6629-0

I. S. Reed and T. K. Truong, The use of finite fields to compute convolutions, IEEE Transactions on Information Theory, vol.21, issue.2, pp.208-213, 1975.
DOI : 10.1109/TIT.1975.1055352

M. C. Schmeling, Corps de transséries, 2001.

A. Schönhage, Multiplikation gro??er Zahlen, Computing, vol.145, issue.3, pp.182-196, 1966.
DOI : 10.1007/BF02234362

A. Schönhage, Storage Modification Machines, SIAM Journal on Computing, vol.9, issue.3, pp.490-508, 1980.
DOI : 10.1137/0209036

A. Schönhage and V. Strassen, Fast multiplication of large numbers, Computing, vol.150, issue.3-4, pp.281-292, 1971.
DOI : 10.1007/BF02242355

I. Shparlinski, On finding primitive roots in finite fields, Theoretical Computer Science, vol.157, issue.2, pp.273-275, 1996.
DOI : 10.1016/0304-3975(95)00164-6

A. L. Toom, The complexity of a scheme of functional elements realizing the multiplication of integers, Soviet Mathematics, vol.4, issue.2, pp.714-716, 1963.

A. L. Toom, Î ñëîaeíîñòè ñõåìû èç ôóíêöèîíàëüíûõ ýëåìåíòîâ, ðåàëèçóþùåé óìíîaeåíèå öåëûõ oeèñåë. Doklady Akad, Nauk SSSR, vol.150, pp.496-498, 1963.

S. Wagstaff, Divisors of Mersenne numbers, Mathematics of Computation, vol.40, issue.161, pp.385-397, 1983.
DOI : 10.1090/S0025-5718-1983-0679454-X

T. Xylouris, On the least prime in an arithmetic progression and estimates for the zeros of Dirichlet Lfunctions, Acta Arith, vol.1, pp.65-91, 2011.