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Publications: 2016-2020  .   2011-2015  .   2006-2010  .   Before 2005  .   Thesis

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2021-2025:Up
  • Approximation of values of algebraic elements over the ring of power sums, joint work with S. Heintze
    J. Théor. Nombres Bordeaux 35 (2023), 63-86
    Preprint: arXiv:2110.09925, Final version: URL

  • A polynomial variant of Diophantine triples in linear recurrences, joint work with S. Heintze
    Period. Math. Hungar. 86 (2023), 289-299
    Preprint: arXiv:2006.12173, Final version: URL

  • On the growth of multi-recurrences, joint work with S. Heintze
    Arch. Math. (Basel) 119 (2022), 489-494
    Preprint: arXiv:2202.03298, Final version: URL

  • Diophantine equations in separated variables and polynomial power sums, joint work with S. Heintze
    Monatsh. Math. 196 (2021), 59-65
    Preprint: arXiv:2008.10342, Final version: URL

  • On the growth of linear recurrences in function fields, joint work with S. Heintze
    Bull. Austr. Math. Soc. 104(1) (2021), 11-20
    Preprint: arXiv:2006.11074, Final version: URL

  • Perfect powers in polynomial power sums, joint work with S. Heintze
    Contemp. Math. 768 (2021), 89-104
    In: "Lie Groups, Number Theory, and Vertex Algebras" (D. Adamovic, A. Dujella, A. Milas, P. Pandzic, eds.), Amer. Math. Soc., 2021
    Preprint: arXiv:1912.10033, Final version: URL

  • Integral zeros of a polynomial with linear recurrences as coefficients, joint work with S. Heintze
    Indag. Math. 32(3) (2021), 691-703
    Preprint: arXiv:2008.10328, Final version: URL

  • Norm form equations with solutions taking values in a multi-recurrence, joint work with S. Heintze
    Acta Arith. 198.4 (2021), 427-438
    Preprint: arXiv:2006.11075, Final version: URL

  • A function field variant of Pillai's problem, joint work with S. Heintze
    J. Number Theory 222 (2021), 278-292
    Preprint: arXiv:2008.10339, Final version: URL

  • Another S-unit variant of Diophantine tuples, joint work with S. Heintze
    Proc. Amer. Math. Soc. 149 (2021), 27-35
    Preprint: arXiv:1910.09285, Final version: URL
2016-2020:Up
  • Algebra (3rd edition), joint book with G. Wüstholz
    Springer Studium Mathematik - Bachelor, Springer Spektrum, Wiesbaden, 2020
    DOI 10.1007/978-3-658-31264-0, URL: ISBN: 978-3-658-31263-3 (Softcover) 978-3-658-31264-0 (eBook)

  • Composite values of polynomial power sums, joint work with C. Karolus
    Ann. Math. Blaise Pascal 26 (2019), 1-24
    Preprint: arXiv:1810.12141

  • Arithmetic and Geometry: Ten Years in Alpbach, edited jointly with G. Wüstholz
    Annals of Mathematics Studies 202, Princeton University Press, Princeton, NJ, 2019
    Final version: URL

  • Decomposable polynomials in second order linear recurrence sequences, joint work with C. Karolus and Dijana Kreso
    Manuscripta Math. 159(3) (2019), 321-346
    Preprint: arXiv:1703.03258, Final version: URL

  • Diophantine triples in linear recurrences of Pisot type, joint work with C. Hutle and Florian Luca
    Res. Number Theory 4 (2018), 4:29
    Preprint: arXiv:1711.04668, Final version: URL

  • Diophantine triples and k-generalized Fibonacci sequences, joint work with C. Hutle, Florian Luca and L. Szalay
    Bull. Malays. Math. Soc. 41 (2018), 1449-1465
    Preprint: arXiv:1602.08236, Final version: URL

  • On fewnomials, integral points, and a toric version of Bertini's theorem, joint work with V. Mantova and U. Zannier
    J. Amer. Math. Soc. 31 (2018), 107-134
    Preprint: arXiv:1412.4548

  • Only finitely many tribonacci Diophantine triples exist, joint work with C. Hutle, N. Irmak, F. Luca, L. Szalay
    Math. Slovaca 67 (2017), 853-862
    Preprint: arXiv:1508.07760, Final version: URL

  • 30 years of collaboration, joint work with L. Hajdu
    Period. Math. Hung. 74 (2017), 255-274
    Preprint: arXiv:1511.07689, Final version: URL

  • Some applications of the p-adic analytic subgroup theorem, joint work with D.H. Pham
    Glasnik Mat. 51(71) (2016), 335-343
    Preprint: arXiv:1412.1248, Final version: URL

  • Elementary resolution of a family of quartic Thue equations over function fields, joint work with R. Paulin and A. Jurasic
    Monatsh. Math. 180 (2016), 205-211
    Preprint: arXiv:1412.3216, Final version: URL
2011-2015:Up
  • Commutative algebraic groups and p-adic linear forms, joint work with D.H. Pham
    Acta Arith. 169 (2015), 115-147
    Preprint: arXiv:1404.4209

  • The p-adic analytic subgroup theorem revisited, joint work with D.H. Pham
    p-Adic Numbers, Ultrametric Analysis and Applications 7 (2015), 143-156
    Preprint: arXiv:1502.00768

  • On Some Applications of Diophantine Aproximations - A translation of C.L. Siegel's Über einige Anwendungen diophantischer Approximationen, with a commentary by C. Fuchs and U. Zannier, edited by U. Zannier
    Edizioni della Normale, Scuola Normale Superiore Pisa, 2014
    URL: ISBN 978-88-7642-519-6 (Softcover) 978-88-7642-520-2 (eBook)

  • Übungen zur Algebra, joint book with G. Wüstholz
    Aufbaukurs Mathematik, Springer Spektrum, Wiesbaden, 2014
    DOI 10.1007/978-3-8348-8679-8, URL: ISBN: 978-3-8348-1962-8 (Softcover) 978-3-8348-8679-8 (eBook)

  • Combinatorial Diophantine equations and a refinement of a theorem on separated variables equations, joint work with Y.F. Bilu, F. Luca and Á. Pintér
    Publ. Math. Debrecen 82/1 (2013), 219-254
    Preprint: (dvi, pdf)

  • On a problem of Diophantus for rationals, joint work with A. Dujella
    J. Number Theory 132 (2012), 2075-2083
    Preprint: (dvi, pdf), Final version: URL

  • Composite rational functions expressible with few terms, joint work with U. Zannier
    J. Eur. Math. Soc. (JEMS) 14 (2012), 175-208
    Preprint: (dvi, pdf)

  • Divisibility properties of hypergeometric polynomials, joint work with T.N. Shorey
    J. Comb. Number Theory 4 (2012), 1-10
    Preprint: (dvi, pdf)

  • Angle trisection with Origami and related topics
    Elem. Math. 66 (2011), 121-136
    Preprint: (dvi, pdf)

  • An effective Shafarevich theorem for elliptic curves, joint work with R. von Känel and G. Wüstholz
    Acta Arith. 148 (2011), 189-203
    Preprint: (dvi, pdf)

  • Composite rational functions having a bounded number of zeros and poles, joint work with A. Pethõ
    Proc. Amer. Math. Soc. 139 (2011), 31-38
    Preprint: (dvi, pdf)
2006-2010:Up
  • Divisibility properties of Generalized Laguerre polynomials, joint work with T.N. Shorey
    Indag. Math. (N.S.) 20 (2) (2009), 217-231
    Preprint: (dvi, pdf)

  • Polynomial-exponential equations involving multi-recurrences
    Studia Sci. Math. Hungar. 46 (2009), 377-398
    Preprint: (dvi, pdf), Final version: URL

  • On quantitative aspects of the unit sum number problem, joint work with R.F. Tichy and V. Ziegler
    Arch. Math. (Basel) 93 (2009), 259-268
    Preprint: (dvi, pdf)

  • Diophantine triples with values in binary recurrences, joint work with F. Luca and L. Szalay
    Ann. Sc. Norm. Super. Pisa Cl. Sc. (5) 7 (2008), 579-608
    Preprint: (dvi, pdf)

  • On the Diophantine equation G_n(x)=G_m(y) with Q(x,y)=0, joint work with A. Pethõ and R. F. Tichy
    Developments in Mathematics 16 (2008), 199-209
    In: ''Diophantine Approximation. Festschrift for Wolfgang Schmidt'' (H.P. Schlickewei, K. Schmidt, R.F. Tichy, eds.), Springer-Verlag, Wien, 2008
    Preprint: (dvi, pdf)

  • A polynomial variant of a problem of Diophantus for pure powers, joint work with A. Dujella and F. Luca
    Int. J. Number Theory 4 (2008), 57-71
    Preprint: (dvi, pdf), Final version: URL

  • On a parametric family of Thue inequalities over function fields, joint work with B. Jadrijevic
    Math. Proc. Camb. Phil. Soc. 143 (2007), 9-23
    Preprint: (dvi, pdf), Final version: URL

  • Effective Solution of the D(-1)-quadruple Conjecture, joint work with A. Dujella and A. Filipin
    Acta Arith. 128 (2007), 319-338
    Preprint: (dvi, pdf), Final version: URL

  • Substitutions, abstract number systems and the space filling property, joint work with R. Tijdeman
    Ann. Inst. Fourier (Grenoble) 56 (2006), 2345-2389
    Preprint: (dvi, pdf), Final version: URL

  • Diophantine m-tuples for linear polynomials. II. Equal degrees, joint work with A. Dujella and P.G. Walsh
    J. Number Theory 120 (2006), 213-228
    Preprint: (dvi, pdf), Final version: URL

  • Thomas's Family of Thue equations over function fields, joint work with  V. Ziegler
    Quart. J. Math. (Oxford) 57 (2006), 81-91
    Preprint: (dvi, pdf), Final version: URL

  • On a family of Thue equations over function fields, joint work with  V. Ziegler
    Monatsh. Math. 147 (2006), 11-23
    Preprint: (dvi, pdf), Final version: URL
Before 2005:Up
  • Effective bounds for the zeros of linear recurrences in function fields, joint work with A. Pethõ
    J. Théor. Nombres Bordeaux 17 (2005), 749-766
    Preprint: (dvi, pdf)

  • Diophantine problems with linear recurrences via the Subspace Theorem
    Integers: Electronic Journal of Combinatorial Number Theory 5(3) (2005), #A08.
    Preprint: (dvi, pdf), Final version: URL

  • Complete solution of a problem of Diophantus and Euler, joint work with A. Dujella
    J. London Math. Soc. (2) 71 (2005), 33-52
    Preprint: (dvi, pdf), Final version: URL

  • Diophantine inequalities involving several power sums, joint work with A. Scremin
    Manuscripta Math. 115 (2004), 163-178
    Preprint: (dvi, pdf)

  • Polynomial-exponential equations involving several linear recurrences, joint work with A. Scremin
    Publ. Math. Debrecen 65/1-2 (2004), 149-172
    Preprint: (dvi, pdf)

  • Complete solution of the polynomial version of a problem of Diophantus, joint work with A. Dujella
    J. Number Theory 106 (2004), 326-344
    Preprint: (dvi, pdf)

  • On the equation G_{n}(x)=G_{m}(P(x)) for third order linear recurring sequences
    Port. Math. (N.S.) 61 (2004), 1-24
    Preprint: (dvi, pdf)

  • Polynomial-exponential equations and linear recurrences
    Glasnik Mat. Ser. III 38 (58) (2003), 233-252
    Preprint: (dvi, pdf)

  • A Polynomial Variant of a Problem of Diophantus and Euler, joint work with A. Dujella
    Rocky Mountain J. Math. 33 (2003), 797-811
    Preprint: (dvi, pdf)

  • On the equation G_{n}(x)=G_{m}(P(x)): Higher order recurrences, joint work with A. Pethõ and R. F. Tichy
    Trans. Amer. Math. Soc. 355 (2003), 4657-4681
    Preprint: (dvi, pdf)

  • An upper bound for the G.C.D. of two linear recurring sequences
    Math. Slovaca 53 (2003), No. 1, 21-42
    Preprint: (dvi, pdf)

  • Perfect powers in linear recurring sequences, joint work with R. F. Tichy
    Acta Arith. 107.1 (2003), 9-25
    Preprint: (dvi, pdf)

  • Diophantine m-tuples for linear polynomials, joint work with A. Dujella and R.F. Tichy
    Period. Math. Hungar. 45 (1-2) (2002), 21-33
    Preprint: (dvi, pdf)

  • On the Diophantine Equation G_{n}(x)=G_{m}(P(x)), joint work with A. Pethõ and R. F. Tichy
    Monatsh. Math. 137 (2002) 3, 173-196
    Preprint: (dvi, pdf)
Thesis:Up
  • Upper Bounds for the Solutions of Diophantine Problems, Habilitation Thesis, TU Graz, 2005.
  • Quantitative finiteness results for Diophantine equations, PhD-Thesis (Dissertation), TU Graz, 2002. (dvi, pdf)
  • Algebraisch-geometrische Codes, Diplomarbeit, TU Wien, 2000. (dvi, pdf)

Impressum    January 10, 2024