JanHendrik Evertse
Preprints and publications 
 
Notes  Preprints  19821985  19861990  19911995  19962000  20012005  20062010  20112015  20162020  
Notes (will probably not be published)  
 
Approximation of complex algebraic numbers by algebraic
numbers of bounded degree.
4 pp. [pdf]  
 
Diophantine equations and Diophantine approximation.
Biennial report 2000&2001 of the
Thomas Stieltjes Institute for Mathematics.
Preprint: [pdf]  
 
A variation on Siegel's Lemma
(Appendix to the paper: "Quantitative Diophantine approximations on projective
varieties" by R.G. Ferretti).
16 pp. [pdf]  
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Preprints  
 
(with K. Győry,
C.L. Stewart)
Mahler's work on Diophantine equations and subsequent developments.
26 pp.
To appear in The Legacy of Kurt Mahler: A Mathematical Selecta, M. Baake, Y. Bugeaud, M. Coons, eds.
Documenta Mathematica, Book Series.
[pdf]  
 
Mahler's work on the geometry of numbers. 17 pp.
To appear in The Legacy of Kurt Mahler: A Mathematical Selecta, M. Baake, Y. Bugeaud, M. Coons, eds.
Documenta Mathematica, Book Series.
[pdf]  
 
The HarderNarasimhan filtration of a multiweighted vector space.
34 pp. [pdf]  
 
The Subspace Theorem and twisted heights. 32 pp. [pdf]  
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Publications 19821985  
[1]  On the equation ax^{n} by^{n}=c, Compos. Math. 47 (1982), 289315.  
[2]  On the representation of integers by binary cubic forms of positive discriminant, Invent. math. 73 (1983), 117138.  
[3]  Upper bounds for the numbers of solutions of Diophantine equations, PhD thesis, MCtract 168, Centrum voor Wiskunde en Informatica, Amsterdam, 1983, 125 pp.  
[4]  On equations in Sunits and the ThueMahler equation, Invent. math. 75 (1984), 561584.  
[5]  On sums of Sunits and linear recurrences, Compos. Math. 53 (1984), 225244.  
[6]  Upper bounds for the numbers of solutions of certain Diophantine equations, Séminaire de Théorie des Nombres, Paris, 198384, C. Goldstein ed. Birkhäuser, Boston etc., 1985, 7190.  
[7]  (with K. Győry) On unit equations and decomposable form equations, J. reine angew. Math. (1985), 619.  
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Publications 19861990 

[8]  (with J.H. Silverman) Uniform bounds for the number of solutions to y^{n}=f(x), Math. Proc. Cambr. Phil. Soc. 100 (1986), 237248.  
[9]  On equations in two Sunits over function fields of characteristic 0, Acta Arith. 47 (1986), 233253.  
[10]  (with D. Chaum) Cryptanalysis of DES with a reduced number of rounds; sequences of linear factors in block ciphers, Proc. Crypto '85, H.C. Williams, ed., Lecture Notes Comp. Sc. 218, Springer Verlag, Berlin 1986, 192211.  
[11]  (with K. Győry, T.N. Shorey, R. Tijdeman) Equal values of binary forms at integral points, Acta Arith. 48 (1987), 379396.  
[12]  (with D. Chaum) A secure and privacyprotecting protocol for transmitting personal information between organizations, Proc. Crypto '86, A.M. Odlyzko, ed., Lecture Notes Comp. Sc. 218, Springer Verlag, Berlin 1986, 118167.  
[13]  (with D. Chaum, J. v.d. Graaf, R. Peralta) Demonstrating possession of a discrete logarithm without revealing it, Proc. Crypto 86, pp. 200212.  
[14]  (with K. Győry) Finiteness criteria for decomposable form equations, Acta Arith. 50 (1988), 357379.  
[15]  (with K. Győry) On the number of polynomials and integral elements of given discriminant, Acta math. Hungar. 51 (1988), 341362.  
[16]  (with K. Győry, C.L. Stewart, R. Tijdeman) Sunit equations in two unknowns, Invent. math. 92 (1988), 461477.  
[17]  (with K. Győry, C.L. Stewart, R. Tijdeman) Sunit equations and their applications, Proc. Conf. Durham 1986, A. Baker, ed., Cambridge 1988, 110174.  
[18]  (with K. Győry) Decomposable form equations, Proc. Conf. Durham 1986, 175202.  
[19]  (with K. Győry) On the numbers of solutions of weighted unit equations, Compos. Math. 66 (1988), 329354.  
[20]  (with D. Chaum, J. v.d. Graaf) An improved protocol for demonstrating possession of discrete logarithms and some generalizations, Proc. Eurocrypt 87, D. Chaum and W.L. Price, eds., Lecture Notes Comp. Sc. 304, Springer Verlag, Berlin, 1988, 127142.  
[21]  Linear structures in blockciphers, Proc. Eurocrypt 87, 249268.  
[22]  Linear structures in blockciphers (revised), CWI Quarterly 1 (1988), 1942.  
[23]  (with I. Gaál, K. Győry) On the numbers of solutions of decomposable polynomial equations, Arch. Math. 52 (1989), 337353.  
[24]  (with K. Győry) ThueMahler equations with a small number of solutions, J. reine angew. Math. 399 (1989), 6080.  
[25]  (with K. Győry) On the number of solutions of unit equations and decomposable polynomial equations, Proc. Conf. Budapest 1987, K. Győry and G. Halász, eds., North Holland, Amsterdam, 1990, 671696.  
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Publications 19911995 

[26]  (with K. Győry) Effective finiteness results for binary forms with given discriminant, Compositio Math. 79 (1991), 169204.  
[27]  (with K. Győry) Some results on Thue equations and ThueMahler equations, Proc. Conf. Computational Number Theory Debrecen 1989, M. Pohst, H. Zimmer, eds., Walter de Gruyter&Co., Berlin, 1991, 295302.  
[28]  (with E. van Heyst) Which new RSA signatures can be computed from some given RSA signatures? Proc. Eurocrypt 90, I.B. Damgård, ed., Lecture Notes Comp. Sc. 473, Springer Verlag, Berlin, 1991, pp. 8397.  
[29]  (with K. Győry) Thue inequalities with a small number of solutions, In: The mathematical heritage of C.F. Gauss, G.M. Rassias, ed., World Scientific, Singapore, 1991, 204224.  
[30]  (with B. Brindza, K. Győry) Bounds for the solutions of some Diophantine equations in terms of discriminants, J. Austral. math. Soc. (Ser. A) 51 (1991), 826.  
[31]  (with K. Győry) Effective finiteness theorems for decomposable forms of given discriminant, Acta Arith. 60 (1992), 233277.  
[32]  (with K. Győry) Discriminants of decomposable forms, in: Analytic and probabilistic methods in number theory, F. Schweiger, E. Manstavicius, eds. VSP Int. Science Publ., Zeist, The Netherlands, 1992, 3956.  
[33]  (with E. van Heyst) Which new RSAsignatures can be computed from certain given RSAsignatures?, J. Cryptology 5 (1992), 4152.  
[34]  Reduced bases of lattices over number fields, Indag. Math. N.S. 3 (1992), 153168.  
[35]  Decomposable form equations with a small linear scattering, J. reine angew. Math. 432 (1992), 177217.  
[36]  Estimates for reduced binary forms, J. reine angew. Math. 434 (1993), 159190.  
[37]  Estimates for discriminants and resultants of binary forms, in: Advances in Number Theory, Proc. CNTA 1991, F.Q. Gouvêa & N. Yui, eds., Clarendon Press, Oxford, 1993, 367380.  
[38]  (with K. Győry): Lower bounds for resultants I, Compositio Math. 88 (1993), 123.  
[39]  (with E. van Heyst): Which new RSAsignatures can be computed from RSAsignatures, obtained in a specific interactive protocol? in: Proc. Eurocrypt 92, R. Rueppel, ed., Lecture Notes Comp. Sc. 658, Springer Verlag, Berlin, etc., 1993, 378391.  
[40]  The Subspace theorem of W.M. Schmidt. In: Diophantine approximation and abelian varieties, proc. conf. Soesterberg 1992, S.J. Edixhoven, J.H. Evertse, eds., Lecture Notes Math. 1566, Springer Verlag, 1993, pp. 3150.  
[41]  An explicit version of Faltings' Product theorem
and an improvement of Roth's
lemma, Acta Arith. 73 (1995), 215248.
Preprint: [ pdf]  
[42]  The number of solutions of decomposable form equations,
Invent. math. 122 (1995),
559601. Preprint: [ pdf]  
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Publications 19962000 

[43]  An improvement of the quantitative Subspace theorem,
Compos. Math. 101 (1996),
225311.
Preprint: [ pdf]  
[44]  (with
R. Tijdeman) Singular differences of powers of
2×2matrices,
Compos. Math. 104 (1996), 199216.
Preprint: [ pdf]  
[45]  The number of solutions of the ThueMahler equation,
J. reine angew. Math. 482 (1997), 121149. Preprint: [ pdf]  
[46]  (with K. Győry): The number of families
of solutions of decomposable form
equations, Acta Arith. 80 (1997), 367394.
Preprint: [ pdf]  
[47]  The number of algebraic numbers of given degree
approximating a given algebraic
number. In: Analytic Number Theory,
proc. conf. Kyoto 1996, Y. Motohashi, ed., pp. 5384. London
Math. Soc. Lecture Note Ser. 247, Cambridge Un. Press, 1997.
Preprint: [ pdf]  
[48]  Lower bounds for
resultants II. In: Number Theory,
Diophantine, Computational and Algebraic Aspects, proc. conf.
Eger 1996, K. Győry,
A. Pethö,
V.T. Sós, eds., pp. 181198.
Walter de Gruyter, 1998.
Preprint: [ pdf]  
[49]  The number of solutions of linear equations in roots of
unity. Acta Arith. 89 (1999), 4551.
Preprint: [ pdf]  
[50]  (with
H.P. Schlickewei): The Absolute Subspace
Theorem and linear equations with unknowns from a multiplicative group.
In: Number Theory in progress, proc. conf. Zakopane 1997 in honour of the 60th
birthday of Prof. Andrzej Schinzel,
K. Győry, H. Iwaniec, J. Urbanowicz, eds.,
pp. 121142. Walter de Gruyter, 1999. Preprint: [ pdf]  
[51]  Symmetric improvements of Liouville's inequality: A survey.
In: Algebraic Number Theory and Diophantine Analysis, Proc. conf. Graz, 1998, F. HalterKoch, R.F. Tichy, eds.,
pp. 129141. Walter de Gruyter, 2000. Preprint: [pdf]  
[52]  On the norm form inequality F(x)≤m,
Publ. Math. Debrecen 56 (2000),
337374
(volume dedicated to the 60th birthday of prof. K. Győry).
Preprint: [pdf]  
[53]  Symmetric improvements of Liouville's inequality.
J. reine angew. Math. 527 (2000), 6995.
Preprint: [pdf]  
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Publications 20012005 

[54]  (with R.G. Ferretti)
Diophantine inequalities on projective varieties.
Intern. Math. Res. Not. 2002:25 (2002), 12951330.
Preprint: [ps]  
[55]  (with
H.P. Schlickewei,
W.M. Schmidt)
Linear equations in variables which lie in a multiplicative group.
Ann. Math. 155 (2002), 130. Preprint: [pdf] Math. arXiv math.NT/0409604  
[56]  (with
H.P. Schlickewei)
A quantitative version of the Absolute Subspace Theorem.
J. reine angew. Math. 548 (2002), 21127. Preprint: [pdf]  
[57]  (with
N. HirataKohno)
Wirsing systems and resultant inequalities.
In: Number Theory for the Millennium, Proc. Millennial Conf. Number Theory, (Urbana, IL, May 2026, 2000), Vol. I,
M.A. Bennett et al. eds., A.K. Peters, 2002, pp. 449461.
Preprint: [pdf]  
[58] 
On resultant inequalities. Acta Arith. 105 (2002), 67101. Preprint: [pdf] 

[59]  Points on subvarieties of tori.
In:
G. Wüstholz, ed., A Panorama in Number Theory or the View from Baker's Garden,
Proc. Conf. Number Theory in honour of the 60th birthday
of Prof. Alan Baker, Zurich, August 30September 4, 1999,
Cambridge Univ. Press, 2002, pp. 214230. Preprint: [pdf]  
[60]  (with
P. Moree,
C.L. Stewart,
R. Tijdeman)
Multivariate Diophantine equations with many solutions.
Acta Arith. 107 (2003), 103125.
Preprint: [pdf] Math. arXiv math.NT/0107219  
[61]  (with
A. Bérczes,
K. Győry)
On the number of equivalence classes of binary forms of given degree
and given discriminant.
Acta Arith. 113 (2004), 363399.
Preprint: [pdf] Math. arXiv math.NT/0312234  
[62] 
Linear equations with unknowns from a multiplicative group whose solutions
lie in a small number of subspaces.
Indag. Math. (NS) 15 (2004), 347355.
Preprint: [pdf] Math. arXiv math.NT/0312235  
[63] 
Distances between the conjugates of an algebraic number.
Publ. Math. Debrecen 65 (2004),
323340 (special volume to the memory of Professor Béla Brindza).
Preprint: Math. arXiv math.NT/0408304 final version: [pdf]  
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Publications 20062010 

[64]  (with
A. Bérczes,
K. Győry)
On the number of pairs of binary forms with given degree
and given resultant, Acta Arith. 128 (2007), 1954.
Preprint: [pdf]  
[65]  (with
A. Bérczes,
K. Győry)
Diophantine problems related to discriminants and resultants of binary forms,
In: Diophantine Geometry, Proceedings of a trimester
held from AprilJuly 2005 at the Scuola Normale Superiore Pisa, U. Zannier, ed.,
Scuola Normale Superiore Pisa, 2007,
pp. 4563.
Preprint: [pdf]  
[66] 
(with R.G. Ferretti)
A generalization of the Subspace Theorem with polynomials of higher degree.
In: Diophantine Approximation, Festschrift for Wolfgang Schmidt,
R.F. Tichy, H.P. Schlickewei, K. Schmidt (eds.),
Proceedings of a conference in honour of Prof. Wolfgang Schmidt's 70th birthday,
held in Vienna, October 610, 2003, Springer Verlag,
2008, pp. 175198.
Preprint: [pdf] Math. arXiv math.NT/0408381  
[67] 
(with
U. Zannier)
Linear equations with unknowns from a multiplicative group in a function field.
Acta Arithmetica 133 (2008), 157170
(volume dedicated to
Wolfgang Schmidt
on the occasion of his 75th birthday).
Preprint: [pdf] Math. arXiv math.NT/0401231  
[68] 
(with Y. Bugeaud)
On two notions of complexity of algebraic numbers.
Acta Arithmetica 133 (2008), 221250
(volume dedicated to
Wolfgang Schmidt
on the occasion of his 75th birthday).
Preprint: [pdf]  
[69] 
(with
A. Bérczes,
K. Győry)
Effective results for linear equations in two unknowns from a multiplicative
division group. Acta Arith. 136 (2009), 331349.
Preprint: [pdf]  
[70] 
(with
A. Bérczes,
K. Győry,
C. Pontreau)
Effective results for points on certain subvarieties of tori.
Math. Proc. Cambridge Philos. Soc. 147 (2009), 6994
Final version: [pdf] (copyright Cambridge University Press)  
[71] 
(with Y. Bugeaud)
Approximation of complex algebraic numbers by algebraic numbers of bounded degree.
Ann. Scuola Norm. Sup. Pisa, Cl. Scienze (5) 8 (2009), 136.
Preprint: [pdf]  
[72] 
On the Quantitative Subspace Theorem.
Zapiski Nauchnyk Seminarov POMI 377 (2010), 217240;
J. Math. Sciences 171 (2010), 824837,
DOI:10.1007/s1095801001856 (copyright Springer Verlag)
Preprint: [pdf]  
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Publications 20112015 

[73] 
A survey on monogenic orders. Dedicated to Kálmán Győry
on his 70th birthday.
Publ. Math. Debrecen 79 (34) (2011), 411422, special volume in honour of
Kálmán Győry, Attila Pethö, János Pintz
and Andras Sarkőzy,
Preprint: [pdf]  
[74] 
(with
K. Győry),
Effective results for unit equations over finitely generated domains.
Math. Proc. Cambridge Phil. Soc. 154 (2013), 351380. DOI:10.1017/S0305004112000606.
Final version: [pdf] (copyright Cambridge University Press).  
[75] 
(with R.G. Ferretti)
A further improvement of the Quantitative Subspace Theorem. Annals of Math. 177 (2013), 513590.
Preprint: [pdf]  
[76] 
(with
A. Bérczes,
K. Győry),
Multiply monogenic orders. Ann. Scuola Norm. Sup. Pisa Cl. Sci (5) (12), 467497.
Preprint: [pdf]  
[77] 
(with
A. Bérczes,
K. Győry),
Effective results for hyper and superelliptic equations over number fields.
Publ. Math. Debrecen 82 (2013), 727756.
Preprint: [pdf]  
[78] 
(with
K. Győry),
Effective results for Diophantine equations over finitely generated domains: A survey.
In: Number theory, analysis and combinatorics, Proceedings of the
Pál Túran Memorial Conference, August 2226, 2011, Budapest,
J. Pintz, A. Biró, K. Győry, G. Harcos, M. Simonovits,
J. Szabados, eds., W. de Gruyter, 2014.
Preprint: [pdf]  
[79] 
(with
A. Bérczes,
K. Győry),
Effective results for Diophantine equations over finitely generated domains. Acta Arith. 163 (2014), 71100.
Preprint: [pdf]  
[80] 
(with K. Győry),
Unit Equations in Diophantine Number Theory,
Cambridge Studies in Advanced Mathematics 146, ISBN 9781107097605,
Cambridge University Press, 2015.
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Publications 20162020 

[81] 
(with K. Győry),
Discriminant Equations in Diophantine Number Theory,
New Mathematical Monographs 32, ISBN 9781107097612,
Cambridge University Press, 2016.
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[82] 
(with S. Akiyama and
A. Pethő)
On nearly linear recurrence sequences.
In: Number Theory  Diophantine Problems, Uniform Distribution and Applications.
Festschrift in Honour of Robert F. Tichy's 60th Birthday, C. Elsholtz, P. Grabner, eds.,
Springer Verlag 2017, pp. 124.
Preprint: [pdf]  
[83] 
(with K. Győry)
Effective results for discriminant equations over finitely generated integral domains.
In: Number Theory  Diophantine Problems, Uniform Distribution and Applications.
Festschrift in Honour of Robert F. Tichy's 60th Birthday, C. Elsholtz, P. Grabner, eds.,
Springer Verlag 2017, pp. 237256.
Preprint: [pdf]  
[84] 
(with Y. Bugeaud)
Sparts of terms of integer linear recurrence sequences.
Mathematika 63 (2017) 840851 (memorial volume for Klaus Friedrich Roth).
Preprint:[pdf]  
[85] 
(with Y. Bugeaud,
K. Győry)
Sparts of values of univariate polynomials, binary forms and decomposable forms
at integral points. Acta Arith. 184 (2018) 151185 (special volume dedicated
to the 75th birthday of Robert Tijdeman).
Preprint: [pdf]  
[86] 
(with K. Győry,
A. Pethő and
Jörg M. Thuswaldner)
Number systems over general orders.
Acta Math. Hungar. 159 (2019), 187205.
Final version: [pdf] (Courtesy of Springer)  
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