Jan-Hendrik Evertse

Preprints and publications

Mathematical Institute |  JHE's homepage
Notes | Preprints  |  1982-1985 |  1986-1990 |  1991-1995 |  1996-2000 |  2001-2005 |  2006-2010 |  2011-2015 |  2016-2020 | 

Notes (will probably not be published)   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 Y. Bugeaud, K. Győry) S-parts of values of univariate polynomials, binary forms and decomposable forms at integral points. 42 pp.
[pdf]
- Mahler's work on the geometry of numbers. 17 pp. To appear in Mahler Selecta, a special volume dedicated to the work of Kurt Mahler.
[pdf]
- (with Y. Bugeaud) S-parts of terms of integer linear recurrence sequences. 13 pp. To appear in Mathematika 63 (2017) (memorial volume for Klaus Friedrich Roth).
[pdf]
- The Harder-Narasimhan filtration of a multi-weighted vector space.  32 pp.
[pdf]
- The Subspace Theorem and twisted heights. 32 pp.
[pdf]
 
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Publications 1982-1985
[1] On the equation axn -byn=c, Compos. Math. 47 (1982), 289-315.
[2] On the representation of integers by binary cubic forms of positive discriminant, Invent. math. 73 (1983), 117-138.
[3] Upper bounds for the numbers of solutions of Diophantine equations, Ph-D thesis, MC-tract 168, Centrum voor Wiskunde en Informatica, Amsterdam, 1983, 125 pp.
[4] On equations in S-units and the Thue-Mahler equation, Invent. math. 75 (1984), 561-584.
[5] On sums of S-units and linear recurrences, Compos. Math. 53 (1984), 225-244.
[6] Upper bounds for the numbers of solutions of certain Diophantine equations, Séminaire de Théorie des Nombres, Paris, 1983-84, C. Goldstein ed. Birkhäuser, Boston etc., 1985, 71-90.
[7] (with K. Győry) On unit equations and decomposable form equations, J. reine angew. Math. (1985), 6-19.
 
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Publications 1986-1990

[8] (with J.H. Silverman) Uniform bounds for the number of solutions to yn=f(x), Math. Proc. Cambr. Phil. Soc. 100 (1986), 237-248.
[9] On equations in two S-units over function fields of characteristic 0, Acta Arith. 47 (1986), 233-253.
[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, 192-211.
[11] (with K. Győry, T.N. Shorey, R. Tijdeman) Equal values of binary forms at integral points, Acta Arith. 48 (1987), 379-396.
[12] (with D. Chaum) A secure and privacy-protecting protocol for transmitting personal information between organizations, Proc. Crypto '86, A.M. Odlyzko, ed., Lecture Notes Comp. Sc. 218, Springer Verlag, Berlin 1986, 118-167.
[13] (with D. Chaum, J. v.d. Graaf, R. Peralta) Demonstrating possession of a discrete logarithm without revealing it, Proc. Crypto 86, pp. 200-212.
[14] (with K. Győry) Finiteness criteria for decomposable form equations, Acta Arith. 50 (1988), 357-379.
[15] (with K. Győry) On the number of polynomials and integral elements of given discriminant, Acta math. Hungar. 51 (1988), 341-362.
[16] (with K. Győry, C.L. Stewart, R. Tijdeman) S-unit equations in two unknowns, Invent. math. 92 (1988), 461-477.
[17] (with K. Győry, C.L. Stewart, R. Tijdeman) S-unit equations and their applications, Proc. Conf. Durham 1986, A. Baker, ed., Cambridge 1988, 110-174.
[18] (with K. Győry) Decomposable form equations, Proc. Conf. Durham 1986, 175-202.
[19] (with K. Győry) On the numbers of solutions of weighted unit equations, Compos. Math. 66 (1988), 329-354.
[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, 127-142.
[21] Linear structures in blockciphers, Proc. Eurocrypt 87, 249-268.
[22] Linear structures in blockciphers (revised), CWI Quarterly 1 (1988), 19-42.
[23] (with I. Gaál, K. Győry) On the numbers of solutions of decomposable polynomial equations, Arch. Math. 52 (1989), 337-353.
[24] (with K. Győry) Thue-Mahler equations with a small number of solutions, J. reine angew. Math. 399 (1989), 60-80.
[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, 671-696.
 
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Publications 1991-1995

[26] (with K. Győry) Effective finiteness results for binary forms with given discriminant, Compositio Math. 79 (1991), 169-204.
[27] (with K. Győry) Some results on Thue equations and Thue-Mahler equations, Proc. Conf. Computational Number Theory Debrecen 1989, M. Pohst, H. Zimmer, eds., Walter de Gruyter&Co., Berlin, 1991, 295-302.
[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. 83-97.
[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, 204-224.
[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), 8-26.
[31] (with K. Győry) Effective finiteness theorems for decomposable forms of given discriminant, Acta Arith. 60 (1992), 233-277.
[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, 39-56.
[33] (with E. van Heyst) Which new RSA-signatures can be computed from certain given RSA-signatures?, J. Cryptology 5 (1992), 41-52.
[34] Reduced bases of lattices over number fields, Indag. Math. N.S. 3 (1992), 153-168.
[35] Decomposable form equations with a small linear scattering, J. reine angew. Math. 432 (1992), 177-217.
[36] Estimates for reduced binary forms, J. reine angew. Math. 434 (1993), 159-190.
[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, 367-380.
[38] (with K. Győry): Lower bounds for resultants I, Compositio Math. 88 (1993), 1-23.
[39] (with E. van Heyst): Which new RSA-signatures can be computed from RSA-signatures, obtained in a specific interactive protocol? in: Proc. Eurocrypt 92, R. Rueppel, ed., Lecture Notes Comp. Sc. 658, Springer Verlag, Berlin, etc., 1993, 378-391.
[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. 31-50.
[41] An explicit version of Faltings' Product theorem and an improvement of Roth's lemma, Acta Arith. 73 (1995), 215-248.
Preprint: [ pdf]
[42] The number of solutions of decomposable form equations, Invent. math. 122 (1995), 559-601.
Preprint: [ pdf]
 
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Publications 1996-2000

[43] An improvement of the quantitative Subspace theorem, Compos. Math. 101 (1996), 225-311.
Preprint: [ pdf]
[44] (with R. Tijdeman) Singular differences of powers of 2×2-matrices, Compos. Math. 104 (1996), 199-216.
Preprint: [ pdf]
[45] The number of solutions of the Thue-Mahler equation, J. reine angew. Math. 482 (1997), 121-149.
Preprint: [ pdf]
[46] (with K. Győry): The number of families of solutions of decomposable form equations, Acta Arith. 80 (1997), 367-394.
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. 53-84. 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. 181-198. Walter de Gruyter, 1998.
Preprint: [ pdf]
[49] The number of solutions of linear equations in roots of unity. Acta Arith. 89 (1999), 45-51.
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. 121-142. 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. Halter-Koch, R.F. Tichy, eds., pp. 129-141. Walter de Gruyter, 2000.
Preprint: [pdf]
[52] On the norm form inequality |F(x)|≤m, Publ. Math. Debrecen 56 (2000), 337-374 (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), 69-95.
Preprint: [pdf]
 
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Publications 2001-2005

[54] (with R.G. Ferretti) Diophantine inequalities on projective varieties. Intern. Math. Res. Not. 2002:25 (2002), 1295-1330.
Preprint: [ps]
[55] (with H.P. Schlickewei, W.M. Schmidt) Linear equations in variables which lie in a multiplicative group. Ann. Math. 155 (2002), 1-30.
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), 21-127.
Preprint: [pdf]
[57] (with N. Hirata-Kohno) Wirsing systems and resultant inequalities. In: Number Theory for the Millennium, Proc. Millennial Conf. Number Theory, (Urbana, IL, May 20-26, 2000), Vol. I, M.A. Bennett et al. eds., A.K. Peters, 2002, pp. 449-461.
Preprint: [pdf]
[58] On resultant inequalities. Acta Arith. 105 (2002), 67-101.
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 30-September 4, 1999, Cambridge Univ. Press, 2002, pp. 214-230.
Preprint: [pdf]
[60] (with P. Moree, C.L. Stewart, R. Tijdeman) Multivariate Diophantine equations with many solutions. Acta Arith. 107 (2003), 103-125.
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), 363-399.
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), 347-355.
Preprint: [pdf]   Math. arXiv math.NT/0312235
[63] Distances between the conjugates of an algebraic number. Publ. Math. Debrecen 65 (2004), 323-340 (special volume to the memory of Professor Béla Brindza).
Preprint: Math. arXiv math.NT/0408304   final version: [pdf]
 
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Publications 2006-2010

[64] (with A. Bérczes, K. Győry) On the number of pairs of binary forms with given degree and given resultant, Acta Arith. 128 (2007), 19-54.
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 April-July 2005 at the Scuola Normale Superiore Pisa, U. Zannier, ed., Scuola Normale Superiore Pisa, 2007, pp. 45-63.
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 6-10, 2003, Springer Verlag, 2008, pp. 175-198.
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), 157-170 (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), 221-250 (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), 331-349.
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), 69-94
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), 1-36.
Preprint: [pdf]
[72] On the Quantitative Subspace Theorem. Zapiski Nauchnyk Seminarov POMI 377 (2010), 217-240; J. Math. Sciences 171 (2010), 824-837, DOI:10.1007/s10958-010-0185-6 (copyright Springer Verlag)
Preprint: [pdf]
 
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Publications 2011-2015

[73] A survey on monogenic orders. Dedicated to Kálmán Győry on his 70th birthday. Publ. Math. Debrecen 79 (3-4) (2011), 411-422, 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), 351-380. 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), 513-590.
Preprint: [pdf]
[76] (with A. Bérczes, K. Győry), Multiply monogenic orders. Ann. Scuola Norm. Sup. Pisa Cl. Sci (5) (12), 467-497.
Preprint: [pdf]
[77] (with A. Bérczes, K. Győry), Effective results for hyper- and superelliptic equations over number fields. Publ. Math. Debrecen 82 (2013), 727-756.
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 22-26, 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), 71-100.
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 2016-2020

[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. 1-24.
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. 237-256.
Preprint: [pdf]
 
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