, Elliptic curves, modular forms and cryptography, Proceedings of the Advanced Instructional Workshop on Algebraic Number Theory, 2003.
Bounding picard numbers of surfaces using p-adic cohomology, Arithmetics, geometry, and coding theory (AGCT 2005), vol.21, pp.125-159, 2010. ,
Some non-special cubic fourfolds ,
Singularities of differentiable maps, Monographs in mathematics, vol.2, 1988. ,
Integer relation detection, Comput. Sci. Eng, vol.2, pp.24-48, 2008. ,
, Compact Complex Surfaces, A Series of Modern Surveys in Mathematics, 2004.
A database of genus-2 curves over the rational numbers, LMS J. Comput. Math, vol.19, pp.235-254, 2016. ,
The Magma algebra system. I. The user language, Computational algebra and number theory, vol.24, pp.235-265, 1993. ,
Creative telescoping for rational functions using the Griffiths-Dwork method, Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation, pp.93-100, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00777675
Knots and numbers in ? 4 theory to 7 loops and beyond, Internat. J. Modern Phys. C, vol.6, pp.519-524, 1995. ,
Mixed tate motives over Z, Ann. of Math, issue.2, pp.949-976, 2012. ,
Numerical computation of endomorphism rings of Jacobians, 13th Algorithmic Number Theory Symposium, vol.2, pp.155-171, 2019. ,
Computing a lattice basis from a system of generating vectors, Lecture Notes in Computer Science, vol.378, pp.54-63, 1989. ,
, On the Picard number of K3 surfaces over number fields, Algebra Number Theory, vol.8, pp.1-17, 2014.
A New View on HJLS and PSLQ: Sums and Projections of Lattices, Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation, ISSAC '13, pp.149-156, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00922192
Computer algebra in the service of mathematical physics and number theory, Computers in Mathematics, vol.125, pp.109-232, 1986. ,
An extension of Zeilberger's fast algorithm to general holonomic functions, Formal power series and algebraic combinatorics, vol.217, pp.115-134, 1997. ,
General components of the Noether-Lefschetz locus and their density in the space of all surfaces, Math. Ann, vol.282, pp.667-680, 1988. ,
Effective computations of Hasse-Weil zeta functions, ProQuest LLC, 2015. ,
Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in p-adic cohomology, 2018. ,
Rigorous computation of the endomorphism ring of a Jacobian, Math. Comp, vol.88, pp.1303-1339, 2019. ,
Computing with Plane Algebraic Curves and Riemann Surfaces: The Algorithms of the Maple Package "Algcurves, pp.67-123, 2011. ,
On the topology of projective subspaces in complex Fermat varieties, J. Math. Soc. Japan, vol.68, pp.975-996, 2016. ,
The Hodge conjecture, in The millennium prize problems, Clay Math. Inst, pp.45-53, 2006. ,
Chern numbers of smooth varieties via homotopy continuation and intersection theory, J. Symb. Comput, vol.46, pp.23-33, 2011. ,
Mirror symmetry for lattice polarized K3 surfaces, J. Math. Sci, vol.81, pp.2599-2630, 1996. ,
, Luigi Cremona (1830-1903) (Italian), vol.36, pp.55-70, 2005.
On the computation of the Picard group for K3 surfaces, Math. Proc. Camb. Philos. Soc, vol.151, pp.263-270, 2011. ,
The picard group of a k3 surface and its reduction modulo p, Algebra Number Theory, vol.5, pp.1027-1040, 2011. ,
Kummer surfaces and the computation of the Picard group, LMS J. Comput. Math, vol.15, pp.84-100, 2012. ,
The PSLQ algorithm for empirical data, Math. Comp, 2018. ,
Analysis of PSLQ, an integer relation finding algorithm, Math. Comput, vol.68, pp.351-370, 1999. ,
Generalization of the Euclidean algorithm for real numbers to all dimensions higher than two, Bull. Am. Math. Soc, vol.1, pp.912-915, 1979. ,
A practical algorithm to compute the geometric Picard lattice of K3 surfaces of degree 2, 2018. ,
Bhabha scattering and a special pencil of K3 surfaces ,
A procedure for determining algebraic integers of given norm, in Computer Algebra, Lecture Notes in Computer Science, pp.194-202, 1983. ,
Soliton equations and their algebro-geometric solutions, of Cambridge Studies in Advanced Mathematics, vol.I, 2003. ,
On the periods of certain rational integrals. I, II, Ann. of Math, issue.2, pp.496-541, 1969. ,
A transcendental method in algebraic geometry, Actes Du Congrès International Des Mathématiciens, vol.1, pp.113-119, 1970. ,
Algebraic Geometry, Graduate Texts in Mathematics, issue.52, 1977. ,
Effective computation of Picard groups and Brauer-Manin obstructions of degree two K3 surfaces over number fields, Rendiconti Circolo Mat. Palermo, vol.62, pp.137-151, 2013. ,
Polynomial time algorithms for finding integer relations among real numbers, SIAM J. Comput, vol.18, pp.859-881, 1989. ,
Numerical Computation of Galois Groups, Found Comput Math, pp.1-24, 2017. ,
, Mirror symmetry, vol.1, 2003.
, , 2002.
, of Cambridge Studies in Advanced Mathematics, vol.158, 2016.
Improved algorithms for integer programming and related lattice problems, Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing, STOC '83, pp.193-206, 1983. ,
Computing zeta functions via p-adic cohomology, Algorithmic number theory, vol.3076, pp.1-17, 2004. ,
A fast approach to creative telescoping, Math. Comput. Sci, vol.4, pp.259-266, 2010. ,
Computing periods of rational integrals, Math. Comput, vol.85, pp.1719-1752, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-00981114
Counting solutions to equations in many variables over finite fields, Found. Comput. Math, vol.4, pp.221-267, 2004. ,
L'analysis situs et la géométrie algébrique, 1950. ,
Factoring polynomials with rational coefficients, Math. Ann, vol.261, pp.515-534, 1982. ,
Computing the geometric endomorphism ring of a genus-2 Jacobian, Math. Comp, vol.88, pp.889-929, 2019. ,
Fermat varieties and the periods of some hypersurfaces, in Algebraic and arithmetic structures of moduli spaces, Adv. Stud. Pure Math., Math. Soc. Japan, vol.58, pp.47-67, 2007. ,
NumGFun: A package for numerical and analytic computation with D-finite functions, Proceedings of the 35th International Symposium on Symbolic and Algebraic Computation, S. M. Watt, pp.139-146, 2010. ,
URL : https://hal.archives-ouvertes.fr/inria-00456983
Rigorous multiple-precision evaluation of D-finite functions in Sagemath, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01342769
A course in Hodge theory ,
Calculation of mixed Hodge structures, Gauss-Manin connections and Picard-Fuchs equations, in Real and Complex Singularities, Trends Math, pp.247-262, 2007. ,
Hermite's Constant and Lattice Algorithms, The LLL Algorithm, pp.19-69, 2009. ,
Computing Gauss-Manin connections for families of projectives hypersurfaces, 2010. ,
Improvements to the deformation method for counting points on smooth projective hypersurfaces, Found. Comput. Math, vol.15, pp.1413-1464, 2015. ,
, Formules de Picard-Lefschetz généralisées et ramification des intégrales, vol.93, pp.333-367, 1965.
, Sur les périodes des intégrales doubles et sur une classe d'équations différentielles linéaires, vol.134, pp.69-71, 1902.
Computing Néron-Severi groups and cycle class groups, Compos. Math, vol.151, pp.713-734, 2015. ,
Variety of power sums and divisors in the moduli space of cubic fourfolds, Doc. Math, vol.22, pp.455-504, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01002965
Linear forms with algebraic coefficients. I, J. Number Theory, vol.3, pp.90001-90002, 1971. ,
Computing periods of hypersurfaces ,
An explicit algorithm for computing the Picard number of certain algebraic surfaces, Amer. J. Math, vol.108, pp.415-432, 1986. ,
Characterization of Jacobian varieties in terms of soliton equations, Invent. Math, vol.83, pp.333-382, 1986. ,
Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components, SIAM J. Numer. Anal, vol.38, pp.2022-2046, 2001. ,
The l-functions and modular forms database, p.16, 2013. ,
, The Sage Developers, SageMath, the Sage Mathematics Software System (Version 8.4), 2018.
Number theory meets high energy physics, Phys. Part. Nuclei Lett, vol.14, pp.291-297, 2017. ,
Periods and special functions in transcendence, Advanced Textbooks in Mathematics, 2017. ,
Fast evaluation of holonomic functions near and in regular singularities, J. Symb. Comput, vol.31, pp.717-743, 2001. ,
On effective analytic continuation, Math. Comput. Sci, vol.1, pp.111-175, 2007. ,
K3 surfaces with Picard number one and infinitely many rational points, Algebra Number Theory, vol.1, pp.1-15, 2007. ,
Examples of genus two CM curves defined over the rationals, Math. Comput, vol.68, pp.307-321, 1999. ,
The physics and the mixed Hodge structure of Feynman integrals, Proceedings of Symposia in Pure Mathematics, vol.88, pp.161-194, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00936661
The Hodge conjecture, Open problems in mathematics, pp.521-543, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-00021776
Hodge groups of K3 surfaces, J. Reine Angew. Math, vol.341, pp.193-220, 1983. ,
Algebraic surfaces, Classics in Mathematics, 1995. ,