GAATI

GAATI Mathematics Laboratory

University of French Polynesia

Publications

David Adam.
Optimalité pour un problème de Bézivin.
Journal de Théorie des Nombres de Bordeaux, volume 31, issue 1, pages 161–177.
Cellule MathDoc/CEDRAM, 2019.
DOI: 10.5802/jtnb.1073

Ethan Berkove, Grant S. Lakeland, Alexander D. Rahm.
The mod 2 cohomology rings of congruence subgroups in the Bianchi groups.
Journal of Algebraic Combinatorics.
Springer Science and Business Media LLC, 2019.
DOI: 10.1007/s10801-019-00912-8

David Adam.
Polynômes à valeurs entières sur des ensembles invariants par rotation.
Journal of Number Theory, volume 186, pages 417–438.
Elsevier BV, 2018.
DOI: 10.1016/j.jnt.2017.10.011

Stéphane Ballet, Alexey Zykin.
Dense families of modular curves, prime numbers and uniform symmetric tensor rank of multiplication in certain finite fields.
Designs, Codes and Cryptography, volume 87, issue 2-3, pages 517–525.
Springer Science and Business Media LLC, 2018.
DOI: 10.1007/s10623-018-0560-8

Gaetan Bisson, Mehdi Tibouchi.
Constructing Permutation Rational Functions from Isogenies.
SIAM Journal on Discrete Mathematics, volume 32, issue 3, pages 1741–1749.
Society for Industrial & Applied Mathematics (SIAM), 2018.
DOI: 10.1137/17m1135736

Philippe Lebacque, Alexey Zykin.
On M-Functions Associated with Modular Forms.
Moscow Mathematical Journal, volume 18, issue 3, pages 437–472.
National Research University, Higher School of Economics (HSE), 2018.
DOI: 10.17323/1609-4514-2018-18-3-437-472

D. Simon, M. Weimann.
Plane curves with minimal discriminant.
Journal of Commutative Algebra, volume 10, issue 4, pages 559–598.
Rocky Mountain Mathematics Consortium, 2018.
DOI: 10.1216/jca-2018-10-4-559

Gaetan Bisson, Marco Streng.
On polarised class groups of orders in quartic CM-fields.
Mathematical Research Letters, volume 24, issue 2, pages 247–270.
International Press of Boston, 2017.
DOI: 10.4310/mrl.2017.v24.n2.a1

Eric Férard.
A infinite class of Kasami functions that are not APN infinitely often.
Contemporary Mathematics, pages 45–63.
American Mathematical Society, 2017.
DOI: 10.1090/conm/686/13777

Eric Férard.
On the irreducibility of the hyperplane sections of Fermat varieties in ℙ 3 P3 in characteristic 2. II.
Cryptography and Communications, volume 9, issue 6, pages 749–767.
Springer Science and Business Media LLC, 2017.
DOI: 10.1007/s12095-017-0213-1

David Adam, Jean-Luc Chabert.
About Number Fields with Pólya Group of Order ≤ 2.
Springer Proceedings in Mathematics & Statistics, pages 23–42.
Springer International Publishing, 2016.
DOI: 10.1007/978-3-319-38855-7_2

Martin Weimann.
Bivariate Factorization Using a Critical Fiber.
Foundations of Computational Mathematics, volume 17, issue 5, pages 1219–1263.
Springer Science and Business Media LLC, 2016.
DOI: 10.1007/s10208-016-9318-8

David Adam, Jean-Luc Chabert.
On Bhargava's factorials of the set of twin primes in ℤ and in 𝔽q[T].
International Journal of Number Theory, volume 11, issue 06, pages 1941–1959.
World Scientific Pub Co Pte Lt, 2015.
DOI: 10.1142/s1793042115500840

David Adam, Michael Welter.
Fonctions entières totales en caractéristique finie.
Bulletin de la Société mathématique de France, volume 143, issue 1, pages 109–124.
Societe Mathematique de France, 2015.
DOI: 10.24033/bsmf.2681

Gaetan Bisson.
Computing endomorphism rings of abelian varieties of dimension two.
Mathematics of Computation, volume 84, issue 294, pages 1977–1989.
American Mathematical Society (AMS), 2015.
DOI: 10.1090/s0025-5718-2015-02938-x

Gerald Bourgeois.
Nonsymmetric generic matrix equations.
Linear Algebra and its Applications, volume 476, pages 159–183.
Elsevier BV, 2015.
DOI: 10.1016/j.laa.2015.03.008

Philippe Lebacque, Alexey Zykin.
On the number of rational points of Jacobians over finite fields.
Acta Arithmetica, volume 169, issue 4, pages 373–384.
Institute of Mathematics, Polish Academy of Sciences, 2015.
DOI: 10.4064/aa169-4-5

Alexey Zykin.
Asymptotic properties of zeta functions over finite fields.
Finite Fields and Their Applications, volume 35, pages 247–283.
Elsevier BV, 2015.
DOI: 10.1016/j.ffa.2015.04.005

Alexey Zykin.
Uniform distribution of zeroes of 𝐿-functions of modular forms.
Contemporary Mathematics, pages 295–299.
American Mathematical Society, 2015.
DOI: 10.1090/conm/637/12762

Gerald Bourgeois.
The Matrix Equation XA-AX=X alpha g(X) over Fields or Rings.
Algebra, volume 2014, pages 1–6.
Hindawi Limited, 2014.
DOI: 10.1155/2014/745029

Christophe Doche.
On the Enumeration of Double-Base Chains with Applications to Elliptic Curve Cryptography.
Lecture Notes in Computer Science, pages 297–316.
Springer Berlin Heidelberg, 2014.
DOI: 10.1007/978-3-662-45611-8_16

Eric Férard.
On the irreducibility of the hyperplane sections of Fermat varieties in P3 in characteristic 2.
Advances in Mathematics of Communications, volume 8, issue 4, pages 497–509.
American Institute of Mathematical Sciences (AIMS), 2014.
DOI: 10.3934/amc.2014.8.497

Florian Luca, Roger Oyono.
The diophantine equation Fyn + Fxn+1 = Fxm.
Integers, volume 2013, pages 479–495.
De Gruyter, 2014.
DOI: 10.1515/9783110298161.479

Stéphane Ballet, Jean Chaumine, Julia Pieltant.
Shimura Modular Curves and Asymptotic Symmetric Tensor Rank of Multiplication in any Finite Field.
Algebraic Informatics, pages 160–172.
Springer Berlin Heidelberg, 2013.
DOI: 10.1007/978-3-642-40663-8_16

Gerald Bourgeois.
Property L And Commuting Exponentials In Dimension At Most Three.
Bulletin of the Australian Mathematical Society, volume 89, issue 1, pages 70–78.
Cambridge University Press (CUP), 2013.
DOI: 10.1017/s0004972713000609

Gerald Bourgeois.
Similar powers of a matrix.
Linear and Multilinear Algebra, volume 61, issue 6, pages 699–709.
Informa UK Limited, 2013.
DOI: 10.1080/03081087.2012.703190

Gérald Bourgeois.
About the matrix function X → AX+XA.
Linear and Multilinear Algebra, volume 62, issue 7, pages 978–987.
Informa UK Limited, 2013.
DOI: 10.1080/03081087.2013.802090

Gérald Bourgeois.
Common invariant subspace and commuting matrices.
Linear Algebra and its Applications, volume 438, issue 7, pages 3030–3038.
Elsevier BV, 2013.
DOI: 10.1016/j.laa.2012.11.034

Florian Luca, Roger Oyono, Aynur Yalciner.
Functions Of Elliptic Curves And Binary Recurrences.
Bulletin of the Australian Mathematical Society, volume 88, issue 3, pages 509–519.
Cambridge University Press (CUP), 2013.
DOI: 10.1017/s0004972713000166

Roger Oyono, Nicolas Thériault.
Group arithmetic inC3,5curves.
Journal of Symbolic Computation, volume 56, pages 1–26.
Elsevier BV, 2013.
DOI: 10.1016/j.jsc.2013.05.008

David Adam, Youssef Fares.
On two affine-like dynamical systems in a local field.
Journal of Number Theory, volume 132, issue 12, pages 2892–2906.
Elsevier BV, 2012.
DOI: 10.1016/j.jnt.2012.05.011

David Adam.
Abel Arithmetic Functions In Finite Characteristic.
International Journal of Number Theory, volume 08, issue 06, pages 1557–1568.
World Scientific Pub Co Pte Lt, 2012.
DOI: 10.1142/s1793042112500959

Eric Férard, Roger Oyono, François Rodier.
Some more functions that are not APN infinitely often. The case of Gold and Kasami exponents.
Contemporary Mathematics, pages 27–36.
American Mathematical Society, 2012.
DOI: 10.1090/conm/574/11423

David Adam, Paul-Jean Cahen.
Newtonian and Schinzel quadratic fields.
Journal of Pure and Applied Algebra, volume 215, issue 8, pages 1902–1918.
Elsevier BV, 2011.
DOI: 10.1016/j.jpaa.2010.11.003

David Adam.
Polynômes à valeurs entières ainsi que leurs dérivées en caractéristique p.
Acta Arithmetica, volume 148, issue 4, pages 351–365.
Institute of Mathematics, Polish Academy of Sciences, 2011.
DOI: 10.4064/aa148-4-3

David Adam.
The Gel'fond-Fridman theorem in positive characteristic.
Israel Journal of Mathematics, volume 185, issue 1, pages 235–251.
Springer Science and Business Media LLC, 2011.
DOI: 10.1007/s11856-011-0108-3

Gerald Bourgeois.
How to solve the matrix equation XA-AX=f(X).
Linear Algebra and its Applications, volume 434, issue 3, pages 657–668.
Elsevier BV, 2011.
DOI: 10.1016/j.laa.2010.09.037

Gerald Bourgeois.
Pairs of matrices, one of which commutes with their commutator.
Electronic Journal of Linear Algebra, volume 22, issue 1.
University of Wyoming Libraries, 2011.
DOI: 10.13001/1081-3810.1460

Gérald Bourgeois, Sébastien Orange.
Dynamical Systems of Simplices in Dimension Two or Three.
Automated Deduction in Geometry, pages 1–21.
Springer Berlin Heidelberg, 2011.
DOI: 10.1007/978-3-642-21046-4_1

Florian Luca, Roger Oyono.
An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers.
Proceedings of the Japan Academy, Series A, Mathematical Sciences, volume 87, issue 4, pages 45–50.
Project Euclid, 2011.
DOI: 10.3792/pjaa.87.45

David Adam, Jean-Luc Chabert, Youssef Fares.
Subsets of ℤ with Simultaneous Orderings.
Integers, volume 10, issue 4.
Walter de Gruyter GmbH, 2010.
DOI: 10.1515/integ.2010.037

David Adam.
Fonctions à valeurs entières et module de Carlitz.
Journal de Théorie des Nombres de Bordeaux, volume 22, issue 2, pages 271–286.
Cellule MathDoc/CEDRAM, 2010.
DOI: 10.5802/jtnb.715

Gerald Bourgeois.
The matrix equation log(XY)=log(X)+log(Y).
Linear Algebra and its Applications, volume 432, issue 8, pages 1878–1884.
Elsevier BV, 2010.
DOI: 10.1016/j.laa.2008.12.024

Eric Férard, François Rodier.
Non linéarité des fonctions booléennes données par des polynômes de degré binaire 3 définies sur 𝔽2𝕞 avec 𝕞 pair.
Contemporary Mathematics, pages 41–53.
American Mathematical Society, 2010.
DOI: 10.1090/conm/521/10272

Enrique González-Jiménez, Roger Oyono.
Non-hyperelliptic modular curves of genus 3.
Journal of Number Theory, volume 130, issue 4, pages 862–878.
Elsevier BV, 2010.
DOI: 10.1016/j.jnt.2009.12.002

Roger Oyono, Christophe Ritzenthaler.
On Rationality of the Intersection Points of a Line with a Plane Quartic.
Arithmetic of Finite Fields, pages 224–237.
Springer Berlin Heidelberg, 2010.
DOI: 10.1007/978-3-642-13797-6_16

David Adam, Youssef Fares.
Integer-valued Euler–Jackson's finite differences.
Monatshefte für Mathematik, volume 161, issue 1, pages 15–32.
Springer Science and Business Media LLC, 2009.
DOI: 10.1007/s00605-009-0111-5

Gerald Bourgeois.
Algebraic systems of matrices and Gröbner basis theory.
Linear Algebra and its Applications, volume 430, issue 8-9, pages 2157–2169.
Elsevier BV, 2009.
DOI: 10.1016/j.laa.2008.11.031

Gérald Bourgeois, Jean-Charles Faugère.
Algebraic attack on NTRU using Witt vectors and Gröbner bases.
Journal of Mathematical Cryptology, volume 3, issue 3.
Walter de Gruyter GmbH, 2009.
DOI: 10.1515/jmc.2009.011

David Adam.
Pólya and Newtonian function fields.
Manuscripta mathematica, volume 126, issue 2, pages 231–246.
Springer Science and Business Media LLC, 2008.
DOI: 10.1007/s00229-008-0173-z

Stéphane Ballet.
A note on the tensor rank of the multiplication in certain finite fields.
Algebraic Geometry and Its Applications.
World Scientific, 2008.
DOI: 10.1142/9789812793430_0017

Stéphane Ballet.
On the tensor rank of the multiplication in the finite fields.
Journal of Number Theory, volume 128, issue 6, pages 1795–1806.
Elsevier BV, 2008.
DOI: 10.1016/j.jnt.2007.06.010

Régis Blache, Éric Férard, Hui June Zhu.
Hodge-Stickelberger polygons for L-functions of exponential sums of P(xs).
Mathematical Research Letters, volume 15, issue 5, pages 1053–1071.
International Press of Boston, 2008.
DOI: 10.4310/mrl.2008.v15.n5.a17

Jean Chaumine.
Multiplication in small finite fields using elliptic curves.
Algebraic Geometry and Its Applications.
World Scientific, 2008.
DOI: 10.1142/9789812793430_0018

Stéphane Flon, Roger Oyono, Christophe Ritzenthaler.
Fast addition on non-hyperelliptic genus 3 curves.
Algebraic Geometry and Its Applications.
World Scientific, 2008.
DOI: 10.1142/9789812793430_0001

Eric Férard, François Rodier.
Non linéarité des fonctions booléennes données par des traces de polynômes de degré binaire 3.
Algebraic Geometry and Its Applications.
World Scientific, 2008.
DOI: 10.1142/9789812793430_0021

Roger Oyono.
Non-hyperelliptic modular Jacobians of dimension 3.
Mathematics of Computation, volume 78, issue 266, pages 1173–1191.
American Mathematical Society (AMS), 2008.
DOI: 10.1090/s0025-5718-08-02174-1

Régis Blache, Jean-Pierre Cherdieu, Jorge Estrada Sarlabous.
Some computational aspects of Jacobians of curves in the family y3=γx5+δ over 𝔽p.
Finite Fields and Their Applications, volume 13, issue 2, pages 348–365.
Elsevier BV, 2007.
DOI: 10.1016/j.ffa.2005.09.003

Régis Blache, Éric Férard.
Newton stratification for polynomials: The open stratum.
Journal of Number Theory, volume 123, issue 2, pages 456–472.
Elsevier BV, 2007.
DOI: 10.1016/j.jnt.2006.06.009

Régis Blache.
On certain character sums overp -adic rings and theirL -functions.
Mathematische Nachrichten, volume 280, issue 15, pages 1681–1697.
Wiley, 2007.
DOI: 10.1002/mana.200510571

Gerald Bourgeois.
On commuting exponentials in low dimensions.
Linear Algebra and its Applications, volume 423, issue 2-3, pages 277–286.
Elsevier BV, 2007.
DOI: 10.1016/j.laa.2006.12.019

R. Granger, F. Hess, R. Oyono, N. Thériault, F. Vercauteren.
Ate Pairing on Hyperelliptic Curves.
Advances in Cryptology - EUROCRYPT 2007, pages 430–447.
Springer Berlin Heidelberg, 2007.
DOI: 10.1007/978-3-540-72540-4_25

S. Ballet, D. Le Brigand.
On the existence of non-special divisors of degree g and g-1 in algebraic functions fields over 𝔽q.
Journal of Number Theory, volume 116, issue 2, pages 293–310.
Elsevier BV, 2006.
DOI: 10.1016/j.jnt.2005.04.009

S. Ballet.
An improvement of the construction of the D.V. and G.V. Chudnovsky algorithm for multiplication in finite fields.
Theoretical Computer Science, volume 352, issue 1-3, pages 293–305.
Elsevier BV, 2006.
DOI: 10.1016/j.tcs.2005.11.045

Jean Chaumine.
Complexité bilinéaire de la multiplication dans des petits corps finis.
Comptes Rendus Mathematique, volume 343, issue 4, pages 265–266.
Elsevier BV, 2006.
DOI: 10.1016/j.crma.2006.06.030

Stéphane Ballet and Robert Rolland. On the bilinear complexity of the multiplication in finite fields. Séminaires et Congrès, volume 11, pages 179–188. Société Mathématique de France, 2005.

Régis Blache.
A Stickelberger theorem for p-adic Gauss sums.
Acta Arithmetica, volume 118, issue 1, pages 11–26.
Institute of Mathematics, Polish Academy of Sciences, 2005.
DOI: 10.4064/aa118-1-2

S. Ballet, R. Rolland.
Multiplication algorithm in a finite field and tensor rank of the multiplication.
Journal of Algebra, volume 272, issue 1, pages 173–185.
Elsevier BV, 2004.
DOI: 10.1016/j.jalgebra.2003.09.031

Stéphane Ballet, Jean Chaumine.
Amélioration des bornes de la complexité bilinéaire de la multiplication dans certains corps finis.
Comptes Rendus Mathematique, volume 339, issue 6, pages 383–385.
Elsevier BV, 2004.
DOI: 10.1016/j.crma.2004.06.011

Stéphane Ballet, Jean Chaumine.
On the Bounds of the Bilinear Complexity of Multiplication in Some Finite Fields.
Applicable Algebra in Engineering, Communication and Computing, volume 15, issue 3-4, pages 205–221.
Springer Science and Business Media LLC, 2004.
DOI: 10.1007/s00200-004-0155-7

Régis Blache.
Exponential sums over lifts of points.
Journal of Number Theory, volume 105, issue 2, pages 361–386.
Elsevier BV, 2004.
DOI: 10.1016/j.jnt.2003.10.004

Stéphane Ballet.
Low increasing tower of algebraic function fields and bilinear complexity of multiplication in any extension of Fq.
Finite Fields and Their Applications, volume 9, issue 4, pages 472–478.
Elsevier BV, 2003.
DOI: 10.1016/s1071-5797(03)00026-1

Eric Férard.
Weight of duals of BCH codes and exponential sums.
Finite Fields and Their Applications, volume 9, issue 1, pages 1–19.
Elsevier BV, 2003.
DOI: 10.1016/s1071-5797(02)00016-3