Bibliography

Major publications by the team in recent years

• 1E. Bayer-Fluckiger, J.-P. Cerri, J. Chaubert.
  
  Euclidean minima and central division algebras, in: International Journal of Number Theory, 2009, vol. 5, n^o 7, pp. 1155–1168.
  
  http://www.worldscinet.com/ijnt/05/0507/S1793042109002614.html
• 2K. Belabas, M. Bhargava, C. Pomerance.
  
  Error estimates for the Davenport-Heilbronn theorems, in: Duke Mathematical Journal, 2010, vol. 153, n^o 1, pp. 173–210.
  
  http://projecteuclid.org/euclid.dmj/1272480934
• 3J. Belding, R. Bröker, A. Enge, K. Lauter.
  
  Computing Hilbert class polynomials, in: Algorithmic Number Theory — ANTS-VIII, Berlin, A. van der Poorten, A. Stein (editors), Lecture Notes in Computer Science, Springer-Verlag, 2007, vol. 5011.
  
  http://hal.inria.fr/inria-00246115
• 4X. Caruso, J. L. Borgne.
  
  A new faster algorithm for factoring skew polynomials over finite fields, in: J. Symbolic Comput., 2018, vol. 79, pp. 411–443.
• 5X. Caruso, D. Roe, T. Vaccon.
  
  Tracking $p$-adic precision, in: LMS J. Comput. Math., 2014, vol. 17, pp. 274–294.
• 6J.-P. Cerri.
  
  Euclidean minima of totally real number fields: algorithmic determination, in: Math. Comp., 2007, vol. 76, n^o 259, pp. 1547–1575.
  
  http://www.ams.org/journals/mcom/2007-76-259/S0025-5718-07-01932-1/
• 7H. Cohen.
  
  Number Theory I: Tools and Diophantine Equations; II: Analytic and Modern Tool, Graduate Texts in Mathematics, Springer-Verlag, New York, 2007, vol. 239/240.
• 8H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen, F. Vercauteren.
  
  Handbook of Elliptic and Hyperelliptic Curve Cryptography, Discrete mathematics and its applications, Chapman & Hall, Boca Raton, 2006.
• 9J.-M. Couveignes, B. Edixhoven.
  
  Computational aspects of modular forms and Galois representations, Princeton University Press, 2011.
• 10A. Enge.
  
  The complexity of class polynomial computation via floating point approximations, in: Mathematics of Computation, 2009, vol. 78, n^o 266, pp. 1089–1107.
  
  http://www.ams.org/mcom/2009-78-266/S0025-5718-08-02200-X/home.html
• 11A. Enge, P. Gaudry, E. Thomé.
  
  An L(1/3) Discrete Logarithm Algorithm for Low Degree Curves, in: Journal of Cryptology, 2011, vol. 24, n^o 1, pp. 24–41.
• 12D. Lubicz, D. Robert.
  
  Computing isogenies between abelian varieties, in: Compositio Mathematica, 09 2012, vol. 148, n^o 05, pp. 1483–1515.
  
  http://dx.doi.org/10.1112/S0010437X12000243

Publications of the year

Doctoral Dissertations and Habilitation Theses

• 13C. Martindale.
  
  Isogeny graphs, modular polynomials, and applications, Université de Bordeaux, June 2018.
  
  https://tel.archives-ouvertes.fr/tel-01992715
• 14A. Riffaut.
  
  Effective computation of special points, Université de Bordeaux, July 2018.
  
  https://tel.archives-ouvertes.fr/tel-01931307

Articles in International Peer-Reviewed Journals

• 15B. Allombert, N. Brisebarre, A. Lasjaunias.
  
  On a two-valued sequence and related continued fractions in power series fields, in: The Ramanujan Journal, 2018, vol. 45, n^o 3, pp. 859-871, https://arxiv.org/abs/1607.07235. [ DOI : 10.1007/s11139-017-9892-7 ]
  
  https://hal.archives-ouvertes.fr/hal-01348576
• 16A. Bartel, A. Page.
  
  Group representations in the homology of 3-manifolds, in: Commentarii Mathematici Helvetici, 2019, https://arxiv.org/abs/1605.04866.
  
  https://hal.inria.fr/hal-01671748
• 17K. Belabas, D. Bernardi, B. Perrin-Riou.
  
  La constante de Manin et le degré modulaire d'une courbe elliptique, in: Publications Mathématiques de Besançon : Algèbre et Théorie des Nombres, 2019.
  
  https://hal.archives-ouvertes.fr/hal-01766202
• 18K. Belabas, H. Cohen.
  
  Modular Forms in Pari/GP, in: Research in the Mathematical Sciences , 2018, https://arxiv.org/abs/1810.00547.
  
  https://hal.inria.fr/hal-01883565
• 19J.-P. Cerri, P. Lezowski.
  
  Computation of Euclidean minima in totally definite quaternion fields, in: International Journal of Number Theory, 2018, 19 pages, some minor corrections; to appear.
  
  https://hal.archives-ouvertes.fr/hal-01447059
• 20A. Enge, W. Hart, F. Johansson.
  
  Short addition sequences for theta functions, in: Journal of Integer Sequences, 2018, vol. 18, n^o 2, pp. 1-34, https://arxiv.org/abs/1608.06810.
  
  https://hal.inria.fr/hal-01355926
• 21F. Johansson, M. Mezzarobba.
  
  Fast and rigorous arbitrary-precision computation of Gauss-Legendre quadrature nodes and weights, in: SIAM Journal on Scientific Computing, 2018, vol. 40, n^o 6, pp. C726-C747, https://arxiv.org/abs/1802.03948. [ DOI : 10.1137/18M1170133 ]
  
  https://hal.inria.fr/hal-01705612
• 22N. Mascot.
  
  Certification of modular Galois representations, in: Mathematics of Computation, 2018, vol. 87, n^o 309, pp. 381–423, https://arxiv.org/abs/1312.6418.
  
  https://hal.archives-ouvertes.fr/hal-01426832
• 23A. Riffaut.
  
  Equations with powers of singular moduli, in: International Journal of Number Theory, 2019, To appear in International Journal of Number Theory.
  
  https://hal.archives-ouvertes.fr/hal-01630363

International Conferences with Proceedings

• 24G. Castagnos, F. Laguillaumie, I. Tucker.
  
  Practical Fully Secure Unrestricted Inner Product Functional Encryption modulo p, in: ASIACRYPT 2018 - 24th International Conference on the Theory and Application of Cryptology and Information Security, Brisbane, Australia, T. Peyri, S. Galbraith (editors), Advances in Cryptology – ASIACRYPT 2018, December 2018, vol. LNCS, n^o 11273, pp. 733-764.
  
  https://hal.archives-ouvertes.fr/hal-01934296
• 25L. De Feo, J. Kieffer, B. Smith.
  
  Towards practical key exchange from ordinary isogeny graphs, in: ASIACRYPT 2018, Brisbane, Australia, December 2018, https://arxiv.org/abs/1809.07543.
  
  https://hal.inria.fr/hal-01872817
• 26F. Johansson.
  
  Numerical integration in arbitrary-precision ball arithmetic, in: Mathematical Software – ICMS 2018, Notre Dame, United States, Lecture Notes in Computer Science, Springer, 2018, n^o 10931, pp. 255–263.
  
  https://hal.inria.fr/hal-01714969

Scientific Books (or Scientific Book chapters)

• 27X. Caruso.
  
  Computations with p-adic numbers, in: Journées Nationales de Calcul Formel, Les cours du CIRM, 2018, https://arxiv.org/abs/1701.06794.
  
  https://hal.archives-ouvertes.fr/hal-01444183
• 28H. Cohen.
  
  An Introduction to Modular Forms, in: Notes from the International School on Computational Number Theory;Izmir Institute of Technology 2017, E. Büyükaik, I. Inam (editors), Springer Birkhäuser, 2018, https://arxiv.org/abs/1809.10907.
  
  https://hal.inria.fr/hal-01883058
• 29H. Cohen.
  
  Computational Number Theory in Relation with L-Functions, in: Notes from the International School on Computational Number Theory; Izmir Institute of Technology 2017, E. Büyükaik, I. Inam (editors), Springer Birkhäuser, 2018, https://arxiv.org/abs/1809.10904.
  
  https://hal.inria.fr/hal-01883052

Other Publications

• 30X. Caruso.
  
  Polynômes de Ore en une variable, January 2018, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01673910
• 31X. Caruso, A. Durand.
  
  Reed-Solomon-Gabidulin Codes, December 2018, https://arxiv.org/abs/1812.09147 - working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01949409
• 32F. Johansson, I. V. Blagouchine.
  
  Computing Stieltjes constants using complex integration, 2018, https://arxiv.org/abs/1804.01679 - working paper or preprint.
  
  https://hal.inria.fr/hal-01758620
• 33F. Johansson.
  
  Numerical Evaluation of Elliptic Functions, Elliptic Integrals and Modular Forms, June 2018, https://arxiv.org/abs/1806.06725 - working paper or preprint.
  
  https://hal.inria.fr/hal-01817952
• 34F. Johansson.
  
  Faster arbitrary-precision dot product and matrix multiplication, January 2019, https://arxiv.org/abs/1901.04289 - working paper or preprint.
  
  https://hal.inria.fr/hal-01980399
• 35E. Lorenzo García, P. Kılıçer, M. Streng.
  
  Primes dividing invariants of CM Picard curves, January 2018, https://arxiv.org/abs/1801.04682 - working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01685037
• 36C. Maire, A. Page.
  
  Codes from unit groups of division algebras over number fields, 2018, https://arxiv.org/abs/1804.07108 - working paper or preprint.
  
  https://hal.inria.fr/hal-01770396
• 37C. Martindale.
  
  Hilbert Modular Polynomials, January 2019, working paper or preprint.
  
  https://hal.inria.fr/hal-01990298

References in notes

• 38K. Belabas.
  
  L'algorithmique de la théorie algébrique des nombres, in: Théorie algorithmique des nombres et équations diophantiennes, N. Berline, A. Plagne, C. Sabbah (editors), 2005, pp. 85–155.
• 39H. Cohen.
  
  Expansions at Cusps and Petersson Products in Pari/GP, in: Elliptic Integrals, Functions, and Modular Forms in Quantum Field Theory, Zeuthen, Germany, Elliptic Integrals, Functions, and Modular Forms in Quantum Field Theory, Springer Wien, October 2017.
  
  https://hal.inria.fr/hal-01883070
• 40H. Cohen, P. Stevenhagen.
  
  Computational class field theory, in: Algorithmic Number Theory — Lattices, Number Fields, Curves and Cryptography, J. Buhler, P. Stevenhagen (editors), MSRI Publications, Cambridge University Press, 2008, vol. 44.
• 41A. Enge.
  
  Courbes algébriques et cryptologie, Université Denis Diderot, Paris 7, 2007, Habilitation à diriger des recherches.
  
  http://tel.archives-ouvertes.fr/tel-00382535/en/
• 42A. Page, A. Bartel.
  
  Torsion homology and regulators of isospectral manifolds, in: Journal of topology, December 2016, vol. 9, n^o 4, pp. 1237 - 1256. [ DOI : 10.1112/jtopol/jtw023 ]
  
  https://hal.inria.fr/hal-01671812