Research Publications
Publications in Refereed Journals
- A. Poëls and D. Roy,
Parametric geometry of numbers over a number field and extension of scalars,
Bulletin de la Société mathématique de France 151 (2023),
257-303.
- J. Champagne and D. Roy,
Diophantine approximation with constraints,
Acta Arithmetica 207 (2023), 57-99, Online First Version.
- A. Poëls and D. Roy,
Simultaneous rational approximation to successive powers of a real number,
Transactions of the American mathematical society 375 (2022), 6385-6415.
- D. Roy,
On the paths of steepest descent for the norm of a one variable complex polynomial,
Proceedings of the American mathematical society 149 (2021), 4863--4869.
- A. Poëls and D. Roy,
Rational approximation to real points on quadratic hypersurfaces,
Journal of the London Mathematical Society 103 (2021), 672--696.
- D. Roy,
Simultaneous approximation to values of the exponential function over the adeles,
Mathematische Annalen, 377 (2020), 1057-1093;
arXiv:1905.01678 [math.NT] (French version: arXiv:1905.00343 [math.NT])
- M. Rivard-Cooke and D. Roy,
Counter-examples in Parametric Geometry of Numbers,
Acta Arithmetica 196.3 (2020), 303-323.
- N. A. V. Nguyen, A. Poëls and D. Roy,
A transference principle for simultaneous rational approximation,
Journal de théorie des nombres de Bordeaux,
32 (2020), 387-402.
- J. Champagne and D. Roy,
A transference inequality for rational approximation to points in geometric progression,
Hardy-Ramanujan Journal, Special Commemorative volume in honour of Alan Baker,
42 (2019), 70-72; hal-02307784v3.
- D. Roy,
A measure of transcendence for singular points on conics,
Journal de théorie des nombres de Bordeaux, 31 (2019), 361-369.
- D. Roy and J. Schleischitz,
Construction of numbers with almost all convergents in a Cantor set,
Canadian Mathematical Bulletin 62 (2019), 869-875;
doi:10.4153/S0008439518000450.
- D. Handelman and D. Roy,
One-sided approximation in affine function spaces,
New York Journal of Mathematics 25 (2019), 374-395.
- S. Pilon et D. Roy,
Construction de nombres extrémaux pour le problème de l'approximation simultanée d'un nombre et de son carré,
Journal de théorie des nombres de Bordeaux 30 (2018), 873--877.
- D. Roy and M. Waldschmidt,
Parametric geometry of numbers in function fields,
Mathematika 63 (2017, special volume in memory of Klaus Roth), 1114-1135.
- D. Roy,
On the topology of Diophantine approximation Spectra,
Compositio Math. 153 (2017), 1512-1546.
- D. Roy,
Spectrum of the exponents of best rational approximation,
Math. Z. 283 (2016), 143-155;
arXiv:1410.1007 .
-
V. Nguyen and D. Roy,
A small value estimate in dimension two involving
translations by rational points,
Int. J. Number Theory,
12 (2016), 1273-1293.
- D. Roy,
On Schmidt and
Summerer parametric geometry of numbers,
Annals of Mathematics 182 (2015), 739-786.
- D. Roy,
Construction of points realizing the regular systems
of Wolfgang Schmidt and Leonard Summerer,
Journal de théorie des nombres de Bordeaux,
27 (2015), 591--603.
- D. Roy,
Diophantine approximation in angular domains,
Monatshefte für Mathematik 173 (2014), 417-432
(the final publication is available at link.springer.com).
- D. Roy,
Une version effective du théorème
de Lindemann-Weierstrass par des méthodes
d'indépendance algébrique,
L'Enseignement Mathématique, Revue Internationale,
59 (2013), 287-306.
- D. Roy,
A small value estimate for Ga x Gm,
Mathematika 59 (2013), 333-363.
- D. Roy,
Rational approximation to real points on conics,
Annales de l'Institut Fourier (Grenoble) 63 (2013), 2331-2348.
- S. Lozier and D. Roy,
Simultaneous approximation to a
real number and to its cube by rational numbers,
Acta Arithmetica 156 (2012), 39-73.
- D. Roy and D. Zelo,
Measures of algebraic approximation to Markoff extremal numbers,
Journal of the London Mathematical Society, 83 (2011), 407-430.
- D. Roy,
Markoff-Lagrange spectrum and extremal numbers,
Acta Mathematica, 206 (2011), 325-362.
- D. Roy,
Small value estimates for the multiplicative group,
Acta Arithmetica, 135.4 (2008), 357-393.
- D. Roy,
Small value estimates for the additive group,
International Journal of Number Theory, 6 (2010) 919-956.
- D. Roy and E. Villani,
On the ring of approximation triples attached to a class of extremal
real numbers, Indagationes Mathematicae, 19 (2008), 299-324.
- D. Roy,
Simultaneous approximation to a real number, its square and its cube
, Acta Arithmetica, 133 (2008), 185-197.
- D. Roy,
On two exponents of approximation related to a real number and its
square, Canadian Journal of Mathematics, 59 (2007), 211-224.
- D. Roy,
Simultaneous approximation by conjugate algebraic numbers
in fields of transcendence degree one, International Journal of Number
Theory, 1 (2005), 357-382.
- D. Roy,
Approximation to real numbers by cubic algebraic integers I, Proceedings of the
London Mathematical Society 88 (2004), 42-62.
- D. Roy
Approximation to real numbers by cubic algebraic integers II,,
Annals of Mathematics 158 (2003), 1081-1087.
- B. Arbour and D. Roy, A Gel'fond type criterion
in degree two, Acta Arithmetica 111 (2004), 97-103.
- D. Roy,
Approximation simultannée d'un nombre et de son carré,
C. R. Acad. Sci. Paris 336 (2003), 1-6.
- D. Roy and M. Waldschmidt, Diophantine approximation
by conjugate algebraic integers, Compositio Mathematica 140 (2004),
593-612.
- D. Roy, Interpolation sur des
perturbations d'ensembles produits, Bulletin de la Société. Mathématique de France 130
(2002), 387-408.
- D. Roy, Interpolation formulas and
auxiliary functions, Journal of Number Theory 94 (2002), 248-285.
- D. Roy, An arithmetic criterion for
the values of the exponential function, Acta Arithmetica 97
(2001),
183-194.
- M. Laurent and D. Roy, Criteria of
algebraic independence with multiplicities and approximation by
hypersurfaces, J. reine angew. Math. 536 (2001), 65-114.
- D. Roy,
Approximation algébrique
simultanée de nombres de Liouville, Canad. Math. Bull. 44
(2001), 115-120.
- M. Laurent et D. Roy, Sur
l'approximation algébrique en degré de transcendance un,
Ann. Inst. Fourier (Grenoble) 49 (1999), 27-55.
- D. Roy and J. L. Thunder, Addendum and
Erratum to: An Absolute Siegel's Lemma, J. reine angew. Math. 508
(1999), 47-51.
- M. Laurent and D. Roy, Criteria of
algebraic independence with multiplicities and interpolation
determinants, Trans. Amer. Math. Soc. 351 (1999), 1845-1870.
- D. Roy et M. Waldschmidt, Approximation
diophantienne et indépendance algébrique de logarithmes, Ann.
Sci. École Norm. Sup. 30 (1997), 753-796.
- D. Roy and M. Waldschmidt, Simultaneous
approximation and algebraic independence, The Ramanujan Journal 1
(1997), 379-430.
- D. Roy and J. L. Thunder, An absolute
Siegel's lemma, J. reine angew. Math. 476 (1996), 1-26.
- D. Roy and J. L. Thunder, Bases of number fields with small
height, Rocky Mountain J. Math. 26 (1996), 1089-1098.
- D. Roy, Points whose coordinates are logarithms of algebraic
numbers on algebraic varieties, Acta Mathematica 175 (1995), 49-73.
- D. Roy and J. L. Thunder, A note on Siegel's lemma over number
fields, Monatsh. Math. 120 (1995), 307-318. (Also available through EuDML.)
- D. Roy and M. Waldschmidt, Quadratic relations between
logarithms of algebraic numbers, Proc. Japan Acad. Ser. A Math. Sci. 71
(1995), 151-153.
- D. Roy et M. Waldschmidt,
Autour du théorème du sous-groupe algébrique, Can. Math. Bull. 36 (1993), 358-367.
- D. Roy, Simultaneous approximation in number fields, Inventiones
Mathematicae 109 (1992), 547-556.
- D. Roy, Matrices whose coefficients are linear forms in
logarithms, J. Number Theory 41 (1992), 22-47.
- D. Roy, Sous-groupes minimaux des groupes de Lie commutatifs
réels, et applications arithmétiques, Acta Arith. 56
(1990),
257-269.
- D. Roy,
Sur une version algébrique de la notion de sous-groupe
minimal, Bull. Soc. Math. France 118 (1990), 171-191.
- D. Roy, Sous-groupes minimaux de Rn, C. R. Acad. Sc.
Paris, Série I, 307 (1988), 423-426.
Papers in preparation or submitted to Refereed Journals
Publications in Refereed Conference Proceedings
- D. Roy
On the continued fraction expansion of a class of
numbers, in: Diophantine approximation, Festschrift for
Wolfgang Schmidt}, Developments in Math. vol. 16,
Eds: H. P. Schlickewei, K. Schmidt and R. Tichy, Springer-Verlag, 2008, 347-361;
arXiv:math.NT/0409233.
- D. Roy
Diophantine approximation in small degree, in: Number Theory, CRM
Proceedings and Lecture Notes 36 (Proceedings of CNTA-7), E. Goren and
H.Kisilevsky Eds, Amer. Math. Soc., Providence, RI, 2004, 269-285;
arXiv:math.NT/0303150.
- D. Roy, Une formule
d'interpolation en deux variables, Journal de théorie des
nombres
de Bordeaux (Proceedings of Journées arithmétiques de
Rome 1999)
13 (2001), 315-323.
- D. Roy, On the v-adic independence of algebraic numbers, in:
Advances in Number Theory (Proc. third Conf. Canadian Number Theory
Association, Kingston, August 1991), F. Q. Gouvêa and N. Yui
eds.,
Clarendon Press, Oxford, 1993, 441-451.
- D. Roy, Transcendance et questions de répartition dans
les
groupes algébriques, in: Approximations diophantiennes et
nombres
transcendants, Luminy 1990, P. Philippon ed., Walter de Gruyter,
Berlin, 1992, 249-274.
- D. Roy,
Matrices dont les coefficients sont des formes linéaires, in: Séminaire de Théorie des Nombres de
Paris
(1987-88), Progress in Math. 81, C. Goldstein ed., Birkhaüser,
New-York, 1990, 273-281.
Chapters in Books
- D. Roy, Zero estimates on commutative algebraic groups,
in: Introduction to algebraic independence theory,
Yu. V. Nesterenko and P. Philippon eds,
Lecture Notes in Mathematics Vol. 1752, Springer-Verlag, Berlin,
2001, 167-185.
- D. Roy, Multiplicity estimate, Chapter VIII of the book
Diophantine Approximation on Linear Algebraic Groups by M. Waldschmidt,
Grundleheren 326, Springer-Verlag, 2000, pp. 231-249.
- D. Roy, Zero estimate, Chapter V of the book Diophantine
Approximation on Linear Algebraic Groups by M. Waldschmidt,
Grundleheren 326, Springer-Verlag, 2000, pp. 147-167.
- D. Roy, Zero estimate, Chapter VIII of the book "Linear
dependence of logarithms of algebraic numbers" by M. Waldschmidt, IMSc
Report 116, Matscience Lecture Notes, Madras, 1992, 14 pages.
Other Publications
- D. Roy, Results and methods of transcendental number theory,
Coxeter-James Lecture, Notices of the Canadian Math. Soc., Vol. 33
no. 2 (2001), 9-14.
- D. Roy, La transcendance de π et la quadrature du cercle,
Gazette des Sciences Mathématiques du Québec, November 1996, 14
pages.
- D. Roy, Sous-groupes minimaux et transcendance, Séminaire
d'arithmétique de St-Etienne 1989-1990, 9 pages.
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