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Author ID: gaal.istvan Recent zbMATH articles by "Gaál, István"
Published as: Gaál, István; Gaál, I.
Homepage: http://math.unideb.hu/gaal-istvan/en
External Links: MGP · Google Scholar · ResearchGate · dblp
Documents Indexed: 90 Publications since 1984, including 3 Books
Reviewing Activity: 343 Reviews
Co-Authors: 21 Co-Authors with 57 Joint Publications
551 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

68 Publications have been cited 399 times in 131 Documents Cited by Year
Diophantine equations and power integral bases. New computational methods. Zbl 1016.11059
Gaál, István
39
2002
Computing all power integral bases in orders of totally real cyclic sextic number fields. Zbl 0857.11069
Gaál, István
20
1996
Computing all power integral bases of cubic fields. Zbl 0677.10013
Gaál, I.; Schulte, N.
20
1989
Integral bases and monogenity of pure fields. Zbl 1419.11118
Gaál, István; Remete, László
19
2017
Simultaneous representation of integers by a pair of ternary quadratic forms – with an application to index form equations in quartic number fields. Zbl 0853.11023
Gaál, István; Pethö, Attila; Pohst, Michael
17
1996
On the resolution of index form equations in biquadratic number fields. III: The bicyclic biquadratic case. Zbl 0853.11026
Gaál, István; Pethö, Attila; Pohst, Michael
15
1995
On the resolution of index form equations in sextic fields with an imaginary quadratic subfield. Zbl 0873.11025
Gaál, István; Pohst, Michael
14
1996
Power integral bases in a parametric family of totally real cyclic quintics. Zbl 0899.11064
Gaál, István; Pohst, Michael
12
1997
On the resolution of relative Thue equations. Zbl 0985.11070
Gaál, István; Pohst, Michael
12
2002
Diophantine equations and power integral bases. Theory and algorithms. 2nd edition. Zbl 1465.11090
Gaál, István
12
2019
On the resolution of index form equations in biquadratic number fields. I. Zbl 0726.11022
Gaál, I.; Pethö, A.; Pohst, M.
11
1991
Power integral bases in orders of composite fields. Zbl 1020.11064
Gaál, István; Olajos, Péter; Pohst, Michael
11
2002
Computing elements of given index in totally complex cyclic sextic fields. Zbl 0857.11068
Gaál, István
9
1995
On the resolution of index form equations in quartic number fields. Zbl 0808.11023
Gaál, István; Pethö, Attila; Pohst, Michael
9
1993
Power integer bases in algebraic number fields. Zbl 0936.11072
Gaál, István
9
1999
Power integral bases in a family of sextic fields with quadratic subfields. Zbl 1393.11068
Gaál, István; Remete, László
9
2015
Computing power integral bases in quartic relative extensions. Zbl 0993.11055
Gaál, István; Pohst, Michael
9
2000
Diophantine equations over global function fields. I: The Thue equation. Zbl 1157.11011
Gaál, István; Pohst, Michael
8
2006
Index form equations in sextic fields: a hard computation. Zbl 1064.11084
Bilu, Yuri; Gaál, István; Győry, Kálmán
8
2004
On the resolution of index form equations in biquadratic number fields. II. Zbl 0726.11023
Gaál, I.; Pethö, A.; Pohst, M.
7
1991
Solving index form equations in fields of degree 9 with cubic subfields. Zbl 0983.11077
Gaál, István
7
2000
Diophantine equations over global function fields. II: \(R\)-integral solutions of Thue equations. Zbl 1142.11019
Gaál, István; Pohst, Michael
7
2006
Binomial Thue equations and power integral bases in pure quartic fields. Zbl 1295.11120
Gaál, István; Remete, László
6
2014
On the resolution of inhomogeneous norm form equations in two dominating variables. Zbl 0654.10020
Gaál, István
5
1988
Power integral bases in composites of number fields. Zbl 0951.11012
Gaál, István
5
1998
Index form equations in quintic fields. Zbl 0930.11091
Gaál, István; Győry, Kálmán
5
1999
Power integral bases in cubic relative extensions. Zbl 1014.11080
Gaál, István
5
2001
On the resolution of resultant type equations. Zbl 1015.11010
Gaál, István
4
2002
Power integral bases in prime-power cyclotomic fields. Zbl 1193.11100
Gaál, István; Robertson, Leanne
4
2006
On the indices of biquadratic number fields having Galois group \(V_ 4\). Zbl 0724.11049
Gaál, I.; Pethö, A.; Pohst, M.
4
1991
Relative power integral bases in infinite families of quartic extensions of quadratic fields. Zbl 1335.11094
Gaál, István; Szabó, Tímea
4
2013
On computing integral points of a Mordell curve over rational function fields in characteristic \(>3\). Zbl 1309.11088
Fieker, Claus; Gaál, István; Pohst, Michael
4
2013
Calculating power integral bases by using relative power integral bases. Zbl 1395.11121
Gaál, István; Remete, László; Szabó, Tímea
4
2016
Diophantine equations over global function fields. IV: S-unit equations in several variables with an application to norm form equations. Zbl 1243.11120
Gaál, István; Pohst, Michael
3
2010
A parametric family of quintic Thue equations. II. Zbl 0995.11024
Gaál, István; Lettl, Günter
3
2000
Calculating “small” solutions of relative Thue equations. Zbl 1390.11067
Gaál, István
3
2015
A note on the minimal indices of pure cubic fields. Zbl 1220.11135
Gaál, István; Szabó, Tímea
3
2010
Integral bases and monogenity of the simplest sextic fields. Zbl 1409.11085
Gaál, István; Remete, László
3
2018
Non-monogenity in a family of octic fields. Zbl 1381.11102
Gaál, István; Remete, László
3
2017
Totally real Thue inequalities over imaginary quadratic fields. Zbl 1455.11052
Gaál, István; Jadrijević, Borka; Remete, László
3
2018
Norm form equations with several dominating variables and explicit lower bounds for inhomogeneous linear forms with algebraic coefficients. I: Effective bounds for the solutions of norm form equations with several dominating variables. Zbl 0612.10012
Gaál, I.
2
1984
On the resolution of index form equations in dihedral quartic number fields. Zbl 0823.11074
Gaál, István; Pethö, Attila; Pohst, Michael
2
1994
On the resolution of some diophantine equations. Zbl 0733.11054
Gaál, I.
2
1991
Inhomogeneous discriminant form equations and integral elements with given discriminant over finitely generated integral domains. Zbl 0626.10015
Gaál, I.
2
1987
Norm form equations with several dominating variables and explicit lower bounds for inhomogeneous linear forms with algebraic coefficients. II. Zbl 0625.10012
Gaál, I.
2
1985
On the resolution of \(F(x,y)=G(x,y)\). Zbl 0789.11022
Gaál, István
2
1993
A fast algorithm for finding “small” solutions of \(F(x,y)= G(x,y)\) over imaginary quadratic fields. Zbl 0806.11018
Gaál, István
2
1993
Diophantine equations over global function fields. III: An application to resultant form equations. Zbl 1233.11036
Gaál, István; Pohst, Michael
2
2008
A parametric family of quintic Thue equations. Zbl 0983.11014
Gaál, István; Lettl, Günter
2
2000
Computing power integral bases in algebraic number fields. Zbl 1011.11067
Gaál, István
2
1998
On the resolution of index form equations. Zbl 0925.11053
Gaál, I.; Pethö, A.; Pohst, M.
2
1991
A fast algorithm for finding small solutions of \(F(x,y)=G(x,y)\) over number fields. Zbl 1072.11095
Gaál, I.
2
2005
Determining elements of minimal index in an infinite family of totally real bicyclic biquadratic number fields. Zbl 1373.11077
Gaál, István; Jadrijević, Borka
2
2017
Solving resultant form equations over number fields. Zbl 1214.11042
Gaál, István; Pohst, Michael
2
2008
Power integral bases in parametric families of biquadratic fields. Zbl 1345.11074
Gaál, István; Szabó, Tímea
2
2012
Simplest quartic and simplest sextic Thue equations over imaginary quadratic fields. Zbl 1479.11054
Gaál, István; Jadrijević, Borka; Remete, László
2
2019
Index form equations in biquadratic fields: the \(p\)-adic case. Zbl 1111.11062
Gaál, István; Nyul, Gábor
1
2006
Inhomogeneous discriminant form and index form equations and their applications. Zbl 0632.10016
Gaál, I.
1
1986
On the numbers of solutions of decomposable polynomial equations. Zbl 0655.10017
Evertse, J. H.; Gaál, I.; Györy, K.
1
1989
Power integral bases in orders of families of quartic fields. Zbl 0814.11051
Gaál, István
1
1993
Computing power integral bases in algebraic number fields. II. Zbl 1011.11068
Gaál, István
1
2000
Application of Thue equations to computing power integral bases in algebraic number fields. Zbl 0891.11062
Gaál, István
1
1996
Recent results on power integral bases of composite fields. Zbl 1101.11012
Gaál, I.; Olajos, P.
1
2003
A remark on prime divisors of lengths of sides of Heron triangles. Zbl 1096.11011
Gaál, István; Járási, István; Luca, Florian
1
2003
On computing integral points of a Mordell curve – the method of Wildanger revisited. Zbl 1465.11237
Gaál, István; Pohst, Maximilian C.; Pohst, Michael E.
1
2021
An experiment on the monogenity of a family of trinomials. Zbl 07523027
Gaál, István
1
2021
Power integral bases in cubic and quartic extensions of real quadratic fields. Zbl 1449.11104
Gaál, István; Remete, László
1
2019
Integral bases and monogenity of composite fields. Zbl 07068036
Gaál, István; Remete, László
1
2019
On computing integral points of a Mordell curve – the method of Wildanger revisited. Zbl 1465.11237
Gaál, István; Pohst, Maximilian C.; Pohst, Michael E.
1
2021
An experiment on the monogenity of a family of trinomials. Zbl 07523027
Gaál, István
1
2021
Diophantine equations and power integral bases. Theory and algorithms. 2nd edition. Zbl 1465.11090
Gaál, István
12
2019
Simplest quartic and simplest sextic Thue equations over imaginary quadratic fields. Zbl 1479.11054
Gaál, István; Jadrijević, Borka; Remete, László
2
2019
Power integral bases in cubic and quartic extensions of real quadratic fields. Zbl 1449.11104
Gaál, István; Remete, László
1
2019
Integral bases and monogenity of composite fields. Zbl 07068036
Gaál, István; Remete, László
1
2019
Integral bases and monogenity of the simplest sextic fields. Zbl 1409.11085
Gaál, István; Remete, László
3
2018
Totally real Thue inequalities over imaginary quadratic fields. Zbl 1455.11052
Gaál, István; Jadrijević, Borka; Remete, László
3
2018
Integral bases and monogenity of pure fields. Zbl 1419.11118
Gaál, István; Remete, László
19
2017
Non-monogenity in a family of octic fields. Zbl 1381.11102
Gaál, István; Remete, László
3
2017
Determining elements of minimal index in an infinite family of totally real bicyclic biquadratic number fields. Zbl 1373.11077
Gaál, István; Jadrijević, Borka
2
2017
Calculating power integral bases by using relative power integral bases. Zbl 1395.11121
Gaál, István; Remete, László; Szabó, Tímea
4
2016
Power integral bases in a family of sextic fields with quadratic subfields. Zbl 1393.11068
Gaál, István; Remete, László
9
2015
Calculating “small” solutions of relative Thue equations. Zbl 1390.11067
Gaál, István
3
2015
Binomial Thue equations and power integral bases in pure quartic fields. Zbl 1295.11120
Gaál, István; Remete, László
6
2014
Relative power integral bases in infinite families of quartic extensions of quadratic fields. Zbl 1335.11094
Gaál, István; Szabó, Tímea
4
2013
On computing integral points of a Mordell curve over rational function fields in characteristic \(>3\). Zbl 1309.11088
Fieker, Claus; Gaál, István; Pohst, Michael
4
2013
Power integral bases in parametric families of biquadratic fields. Zbl 1345.11074
Gaál, István; Szabó, Tímea
2
2012
Diophantine equations over global function fields. IV: S-unit equations in several variables with an application to norm form equations. Zbl 1243.11120
Gaál, István; Pohst, Michael
3
2010
A note on the minimal indices of pure cubic fields. Zbl 1220.11135
Gaál, István; Szabó, Tímea
3
2010
Diophantine equations over global function fields. III: An application to resultant form equations. Zbl 1233.11036
Gaál, István; Pohst, Michael
2
2008
Solving resultant form equations over number fields. Zbl 1214.11042
Gaál, István; Pohst, Michael
2
2008
Diophantine equations over global function fields. I: The Thue equation. Zbl 1157.11011
Gaál, István; Pohst, Michael
8
2006
Diophantine equations over global function fields. II: \(R\)-integral solutions of Thue equations. Zbl 1142.11019
Gaál, István; Pohst, Michael
7
2006
Power integral bases in prime-power cyclotomic fields. Zbl 1193.11100
Gaál, István; Robertson, Leanne
4
2006
Index form equations in biquadratic fields: the \(p\)-adic case. Zbl 1111.11062
Gaál, István; Nyul, Gábor
1
2006
A fast algorithm for finding small solutions of \(F(x,y)=G(x,y)\) over number fields. Zbl 1072.11095
Gaál, I.
2
2005
Index form equations in sextic fields: a hard computation. Zbl 1064.11084
Bilu, Yuri; Gaál, István; Győry, Kálmán
8
2004
Recent results on power integral bases of composite fields. Zbl 1101.11012
Gaál, I.; Olajos, P.
1
2003
A remark on prime divisors of lengths of sides of Heron triangles. Zbl 1096.11011
Gaál, István; Járási, István; Luca, Florian
1
2003
Diophantine equations and power integral bases. New computational methods. Zbl 1016.11059
Gaál, István
39
2002
On the resolution of relative Thue equations. Zbl 0985.11070
Gaál, István; Pohst, Michael
12
2002
Power integral bases in orders of composite fields. Zbl 1020.11064
Gaál, István; Olajos, Péter; Pohst, Michael
11
2002
On the resolution of resultant type equations. Zbl 1015.11010
Gaál, István
4
2002
Power integral bases in cubic relative extensions. Zbl 1014.11080
Gaál, István
5
2001
Computing power integral bases in quartic relative extensions. Zbl 0993.11055
Gaál, István; Pohst, Michael
9
2000
Solving index form equations in fields of degree 9 with cubic subfields. Zbl 0983.11077
Gaál, István
7
2000
A parametric family of quintic Thue equations. II. Zbl 0995.11024
Gaál, István; Lettl, Günter
3
2000
A parametric family of quintic Thue equations. Zbl 0983.11014
Gaál, István; Lettl, Günter
2
2000
Computing power integral bases in algebraic number fields. II. Zbl 1011.11068
Gaál, István
1
2000
Power integer bases in algebraic number fields. Zbl 0936.11072
Gaál, István
9
1999
Index form equations in quintic fields. Zbl 0930.11091
Gaál, István; Győry, Kálmán
5
1999
Power integral bases in composites of number fields. Zbl 0951.11012
Gaál, István
5
1998
Computing power integral bases in algebraic number fields. Zbl 1011.11067
Gaál, István
2
1998
Power integral bases in a parametric family of totally real cyclic quintics. Zbl 0899.11064
Gaál, István; Pohst, Michael
12
1997
Computing all power integral bases in orders of totally real cyclic sextic number fields. Zbl 0857.11069
Gaál, István
20
1996
Simultaneous representation of integers by a pair of ternary quadratic forms – with an application to index form equations in quartic number fields. Zbl 0853.11023
Gaál, István; Pethö, Attila; Pohst, Michael
17
1996
On the resolution of index form equations in sextic fields with an imaginary quadratic subfield. Zbl 0873.11025
Gaál, István; Pohst, Michael
14
1996
Application of Thue equations to computing power integral bases in algebraic number fields. Zbl 0891.11062
Gaál, István
1
1996
On the resolution of index form equations in biquadratic number fields. III: The bicyclic biquadratic case. Zbl 0853.11026
Gaál, István; Pethö, Attila; Pohst, Michael
15
1995
Computing elements of given index in totally complex cyclic sextic fields. Zbl 0857.11068
Gaál, István
9
1995
On the resolution of index form equations in dihedral quartic number fields. Zbl 0823.11074
Gaál, István; Pethö, Attila; Pohst, Michael
2
1994
On the resolution of index form equations in quartic number fields. Zbl 0808.11023
Gaál, István; Pethö, Attila; Pohst, Michael
9
1993
On the resolution of \(F(x,y)=G(x,y)\). Zbl 0789.11022
Gaál, István
2
1993
A fast algorithm for finding “small” solutions of \(F(x,y)= G(x,y)\) over imaginary quadratic fields. Zbl 0806.11018
Gaál, István
2
1993
Power integral bases in orders of families of quartic fields. Zbl 0814.11051
Gaál, István
1
1993
On the resolution of index form equations in biquadratic number fields. I. Zbl 0726.11022
Gaál, I.; Pethö, A.; Pohst, M.
11
1991
On the resolution of index form equations in biquadratic number fields. II. Zbl 0726.11023
Gaál, I.; Pethö, A.; Pohst, M.
7
1991
On the indices of biquadratic number fields having Galois group \(V_ 4\). Zbl 0724.11049
Gaál, I.; Pethö, A.; Pohst, M.
4
1991
On the resolution of some diophantine equations. Zbl 0733.11054
Gaál, I.
2
1991
On the resolution of index form equations. Zbl 0925.11053
Gaál, I.; Pethö, A.; Pohst, M.
2
1991
Computing all power integral bases of cubic fields. Zbl 0677.10013
Gaál, I.; Schulte, N.
20
1989
On the numbers of solutions of decomposable polynomial equations. Zbl 0655.10017
Evertse, J. H.; Gaál, I.; Györy, K.
1
1989
On the resolution of inhomogeneous norm form equations in two dominating variables. Zbl 0654.10020
Gaál, István
5
1988
Inhomogeneous discriminant form equations and integral elements with given discriminant over finitely generated integral domains. Zbl 0626.10015
Gaál, I.
2
1987
Inhomogeneous discriminant form and index form equations and their applications. Zbl 0632.10016
Gaál, I.
1
1986
Norm form equations with several dominating variables and explicit lower bounds for inhomogeneous linear forms with algebraic coefficients. II. Zbl 0625.10012
Gaál, I.
2
1985
Norm form equations with several dominating variables and explicit lower bounds for inhomogeneous linear forms with algebraic coefficients. I: Effective bounds for the solutions of norm form equations with several dominating variables. Zbl 0612.10012
Gaál, I.
2
1984
all top 5

Cited by 107 Authors

36 Gaál, István
15 Pohst, Michael E.
10 Pethő, Attila
7 Jones, Lenny K.
7 Nakahara, Toru
7 Remete, László
6 El Fadil, Lhoussain
6 Ziegler, Volker
5 Robertson, Leanne
4 Bennett, Michael A.
4 Heuberger, Clemens
4 Hoshi, Akinari
4 Jadrijević, Borka
4 Spearman, Blair Kenneth
3 Ben Yakkou, Hamid
3 Fieker, Claus
3 Nyul, Gábor
3 Smith, Hanson
2 Ahmad, Shahzad
2 Arnóczki, Tímea
2 Brunotte, Horst
2 Evertse, Jan-Hendrik
2 Gassert, Thomas Alden
2 Ghadermarzi, Amir
2 Győry, Kálmán
2 Harrington, Joshua
2 Jakhar, Anuj
2 Járási, István
2 Lettl, Günter Hermann Alexander
2 Poulakis, Dimitrios
2 Shah, Syed Inayat Ali
2 Tichy, Robert Franz
2 Togbé, Alain
2 Williams, Kenneth S.
1 Acciaro, Vincenzo
1 Akhtari, Shabnam
1 Akiyama, Shigeki
1 Alkabouss, Sakha A.
1 Alvanos, Paraskevas
1 Aygin, Zafer Selçuk
1 Bae, Sunghan
1 Bayad, Abdelmejid
1 Bellah, Elisa
1 Bérczes, Attila
1 Brindza, Béla
1 Chang, Mu-Ling
1 Chillali, Abdelhakim
1 Cremona, John E.
1 Davis, Chad Tyler
1 Didi, Jalal
1 Draziotis, Konstantinos A.
1 Dujella, Andrej
1 Fermigier, Stéfane
1 Garici, Tarek
1 Gras, Marie-Nicole
1 Hajdu, Lajos
1 Hameed, Abdul
1 He, Bo
1 Hu, Su
1 Husnine, Syed Muhammad
1 Huszti, Andrea
1 Jacobson, Michael John jun.
1 Jung, Ho Yun
1 Karemaker, Valentijn
1 Katayama, Shin-ichi
1 Khan, Nadia
1 Kim, Henry H.
1 Koo, Jakyung
1 Larone, Jesse
1 Lavallee, Melisa J.
1 Lee, Yoonjin
1 Leprévost, Franck
1 Li, Yan
1 Louboutin, Stéphane R.
1 Luca, Florian
1 Łysik, Grzegorz
1 Madritsch, Manfred G.
1 Marques, Sophie
1 Mignotte, Maurice
1 Miller-Sims, Laurel
1 Motoda, Yasuo
1 Nakano, Shin-ichi
1 Olajos, Péter
1 Petrányi, Gábor
1 Phillips, Tristan
1 Ranieri, Gabriele
1 Ratliff, Louis J. jun.
1 Roth, Ralf
1 Rush, David E.
1 Rusin, D.
1 Scheidler, Renate
1 Scholl, Travis
1 Seddik, Mohammed
1 Shah, Kishor
1 Shin, Dong Hwa
1 Sijsling, Jeroen
1 Smart, Nigel P.
1 Stange, Katherine E.
1 Sultan, Mamoona
1 Surer, Paul
...and 7 more Authors
all top 5

Cited in 41 Serials

31 Journal of Number Theory
10 International Journal of Number Theory
8 Mathematics of Computation
7 Acta Mathematica Hungarica
7 Journal de Théorie des Nombres de Bordeaux
6 Journal of Symbolic Computation
5 Periodica Mathematica Hungarica
5 Rocky Mountain Journal of Mathematics
5 Functiones et Approximatio. Commentarii Mathematici
5 Experimental Mathematics
4 Acta Arithmetica
3 Acta Mathematica et Informatica Universitatis Ostraviensis
2 International Journal of Mathematics
2 JP Journal of Algebra, Number Theory and Applications
1 Bulletin of the Australian Mathematical Society
1 Communications in Algebra
1 Journal of Mathematical Analysis and Applications
1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
1 Acta Scientiarum Mathematicarum
1 Archiv der Mathematik
1 Compositio Mathematica
1 Czechoslovak Mathematical Journal
1 Kodai Mathematical Journal
1 Manuscripta Mathematica
1 Mathematica Slovaca
1 Monatshefte für Mathematik
1 Nagoya Mathematical Journal
1 Proceedings of the American Mathematical Society
1 Transactions of the American Mathematical Society
1 Revista Matemática Iberoamericana
1 International Journal of Algebra and Computation
1 Elemente der Mathematik
1 Glasnik Matematički. Serija III
1 Annales Mathématiques Blaise Pascal
1 The New York Journal of Mathematics
1 Boletín de la Sociedad Matemática Mexicana. Third Series
1 Taiwanese Journal of Mathematics
1 LMS Journal of Computation and Mathematics
1 Journal of Algebra and its Applications
1 Journal of Mathematical Cryptology
1 Applicable Analysis and Discrete Mathematics

Citations by Year