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## Gaál, István

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 Author ID: gaal.istvan Published as: Gaál, I.; Gaál, István Homepage: http://math.unideb.hu/gaal-istvan/en External Links: MGP · ResearchGate · dblp
 Documents Indexed: 84 Publications since 1984, including 3 Books Reviewing Activity: 306 Reviews
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#### Co-Authors

 29 single-authored 25 Pohst, Michael E. 12 Remete, László 8 Pethő, Attila 5 Szabó, Tímea 4 Győry, Kálmán 3 Jadrijević, Borka 2 Lettl, Günter Hermann Alexander 2 Nyul, Gábor 2 Olajos, Péter 1 Bilu, Yuri F. 1 Brindza, Béla 1 Everest, Graham Robert 1 Evertse, Jan-Hendrik 1 Fieker, Claus 1 Járási, István 1 Luca, Florian 1 Petrányi, Gábor 1 Pohst, Maximilian C. 1 Robertson, Leanne 1 Röttger, Christian 1 Schulte, Nils
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#### Serials

 10 Journal of Number Theory 8 Mathematics of Computation 8 Experimental Mathematics 8 JP Journal of Algebra, Number Theory and Applications 7 Journal of Symbolic Computation 5 Publicationes Mathematicae 4 Acta Arithmetica 3 Functiones et Approximatio. Commentarii Mathematici 3 Acta Mathematica Hungarica 2 Archiv der Mathematik 2 Studia Scientiarum Mathematicarum Hungarica 2 Tatra Mountains Mathematical Publications 1 Rocky Mountain Journal of Mathematics 1 Acta Scientiarum Mathematicarum 1 Canadian Mathematical Bulletin 1 Czechoslovak Mathematical Journal 1 Mathematica Slovaca 1 Monatshefte für Mathematik 1 Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio Computatorica 1 Glasnik Matematički. Serija III 1 Journal de Théorie des Nombres de Bordeaux 1 Acta Academiae Paedagogicae Agriensis. Nova Series. Sectio Matematicae 1 International Journal of Pure and Applied Mathematics 1 International Journal of Number Theory 1 Journal of Mathematical Cryptology

#### Fields

 84 Number theory (11-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH Open

64 Publications have been cited 326 times in 110 Documents Cited by Year
Diophantine equations and power integral bases. New computational methods. Zbl 1016.11059
Gaál, István
2002
Computing all power integral bases of cubic fields. Zbl 0677.10013
Gaál, I.; Schulte, N.
1989
Computing all power integral bases in orders of totally real cyclic sextic number fields. Zbl 0857.11069
Gaál, István
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
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
1995
On the resolution of index form equations in sextic fields with an imaginary quadratic subfield. Zbl 0873.11025
Gaál, István; Pohst, Michael
1996
On the resolution of relative Thue equations. Zbl 0985.11070
Gaál, István; Pohst, Michael
2002
Power integral bases in a parametric family of totally real cyclic quintics. Zbl 0899.11064
Gaál, István; Pohst, Michael
1997
On the resolution of index form equations in biquadratic number fields. I. Zbl 0726.11022
Gaál, I.; Pethö, A.; Pohst, M.
1991
On the resolution of index form equations in quartic number fields. Zbl 0808.11023
Gaál, István; Pethö, Attila; Pohst, Michael
1993
Diophantine equations over global function fields. I: The Thue equation. Zbl 1157.11011
Gaál, István; Pohst, Michael
2006
Computing elements of given index in totally complex cyclic sextic fields. Zbl 0857.11068
Gaál, István
1995
Integral bases and monogenity of pure fields. Zbl 1419.11118
Gaál, István; Remete, László
2017
Diophantine equations over global function fields. II: $$R$$-integral solutions of Thue equations. Zbl 1142.11019
Gaál, István; Pohst, Michael
2006
Computing power integral bases in quartic relative extensions. Zbl 0993.11055
Gaál, István; Pohst, Michael
2000
Solving index form equations in fields of degree 9 with cubic subfields. Zbl 0983.11077
Gaál, István
2000
Power integral bases in orders of composite fields. Zbl 1020.11064
Gaál, István; Olajos, Péter; Pohst, Michael
2002
Power integral bases in composites of number fields. Zbl 0951.11012
Gaál, István
1998
On the resolution of index form equations in biquadratic number fields. II. Zbl 0726.11023
Gaál, I.; Pethö, A.; Pohst, M.
1991
Index form equations in quintic fields. Zbl 0930.11091
Gaál, István; Győry, Kálmán
1999
Power integral bases in a family of sextic fields with quadratic subfields. Zbl 1393.11068
Gaál, István; Remete, László
2015
Power integral bases in prime-power cyclotomic fields. Zbl 1193.11100
Gaál, István; Robertson, Leanne
2006
Index form equations in sextic fields: a hard computation. Zbl 1064.11084
Bilu, Yuri; Gaál, István; Győry, Kálmán
2004
Power integral bases in cubic relative extensions. Zbl 1014.11080
Gaál, István
2001
Power integer bases in algebraic number fields. Zbl 0936.11072
Gaál, István
1999
On the indices of biquadratic number fields having Galois group $$V_ 4$$. Zbl 0724.11049
Gaál, I.; Pethö, A.; Pohst, M.
1991
On the resolution of inhomogeneous norm form equations in two dominating variables. Zbl 0654.10020
Gaál, István
1988
Binomial Thue equations and power integral bases in pure quartic fields. Zbl 1295.11120
Gaál, István; Remete, László
2014
Relative power integral bases in infinite families of quartic extensions of quadratic fields. Zbl 1335.11094
Gaál, István; Szabó, Tímea
2013
A note on the minimal indices of pure cubic fields. Zbl 1220.11135
Gaál, István; Szabó, Tímea
2010
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
2010
Diophantine equations over global function fields. III: An application to resultant form equations. Zbl 1233.11036
Gaál, István; Pohst, Michael
2008
On the resolution of resultant type equations. Zbl 1015.11010
Gaál, István
2002
A parametric family of quintic Thue equations. II. Zbl 0995.11024
Gaál, István; Lettl, Günter
2000
Computing power integral bases in algebraic number fields. Zbl 1011.11067
Gaál, István
1998
Diophantine equations and power integral bases. Theory and algorithms. 2nd edition. Zbl 07077014
Gaál, István
2019
Determining elements of minimal index in an infinite family of totally real bicyclic biquadratic number fields. Zbl 1373.11077
2017
Non-monogenity in a family of octic fields. Zbl 1381.11102
Gaál, István; Remete, László
2017
Calculating power integral bases by using relative power integral bases. Zbl 1395.11121
Gaál, István; Remete, László; Szabó, Tímea
2016
On computing integral points of a Mordell curve over rational function fields in characteristic $$>3$$. Zbl 1309.11088
Fieker, Claus; Gaál, István; Pohst, Michael
2013
Power integral bases in parametric families of biquadratic fields. Zbl 1345.11074
Gaál, István; Szabó, Tímea
2012
A parametric family of quintic Thue equations. Zbl 0983.11014
Gaál, István; Lettl, Günter
2000
On the resolution of index form equations in dihedral quartic number fields. Zbl 0823.11074
Gaál, István; Pethö, Attila; Pohst, Michael
1994
On the resolution of some diophantine equations. Zbl 0733.11054
Gaál, I.
1991
On the resolution of index form equations. Zbl 0925.11053
Gaál, I.; Pethö, A.; Pohst, M.
1991
Inhomogeneous discriminant form equations and integral elements with given discriminant over finitely generated integral domains. Zbl 0626.10015
Gaál, I.
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.
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.
1984
Power integral bases in cubic and quartic extensions of real quadratic fields. Zbl 1449.11104
Gaál, István; Remete, László
2019
Integral bases and monogenity of composite fields. Zbl 07068036
Gaál, István; Remete, László
2019
Integral bases and monogenity of the simplest sextic fields. Zbl 1409.11085
Gaál, István; Remete, László
2018
Calculating “small” solutions of relative Thue equations. Zbl 1390.11067
Gaál, István
2015
Solving resultant form equations over number fields. Zbl 1214.11042
Gaál, István; Pohst, Michael
2008
Index form equations in biquadratic fields: the $$p$$-adic case. Zbl 1111.11062
Gaál, István; Nyul, Gábor
2006
A fast algorithm for finding small solutions of $$F(x,y)=G(x,y)$$ over number fields. Zbl 1072.11095
Gaál, I.
2005
A remark on prime divisors of lengths of sides of Heron triangles. Zbl 1096.11011
Gaál, István; Járási, István; Luca, Florian
2003
Recent results on power integral bases of composite fields. Zbl 1101.11012
Gaál, I.; Olajos, P.
2003
Computing power integral bases in algebraic number fields. II. Zbl 1011.11068
Gaál, István
2000
Application of Thue equations to computing power integral bases in algebraic number fields. Zbl 0891.11062
Gaál, István
1996
Power integral bases in orders of families of quartic fields. Zbl 0814.11051
Gaál, István
1993
A fast algorithm for finding “small” solutions of $$F(x,y)= G(x,y)$$ over imaginary quadratic fields. Zbl 0806.11018
Gaál, István
1993
On the resolution of $$F(x,y)=G(x,y)$$. Zbl 0789.11022
Gaál, István
1993
On the numbers of solutions of decomposable polynomial equations. Zbl 0655.10017
Evertse, J. H.; Gaál, I.; Györy, K.
1989
Inhomogeneous discriminant form and index form equations and their applications. Zbl 0632.10016
Gaál, I.
1986
Diophantine equations and power integral bases. Theory and algorithms. 2nd edition. Zbl 07077014
Gaál, István
2019
Power integral bases in cubic and quartic extensions of real quadratic fields. Zbl 1449.11104
Gaál, István; Remete, László
2019
Integral bases and monogenity of composite fields. Zbl 07068036
Gaál, István; Remete, László
2019
Integral bases and monogenity of the simplest sextic fields. Zbl 1409.11085
Gaál, István; Remete, László
2018
Integral bases and monogenity of pure fields. Zbl 1419.11118
Gaál, István; Remete, László
2017
Determining elements of minimal index in an infinite family of totally real bicyclic biquadratic number fields. Zbl 1373.11077
2017
Non-monogenity in a family of octic fields. Zbl 1381.11102
Gaál, István; Remete, László
2017
Calculating power integral bases by using relative power integral bases. Zbl 1395.11121
Gaál, István; Remete, László; Szabó, Tímea
2016
Power integral bases in a family of sextic fields with quadratic subfields. Zbl 1393.11068
Gaál, István; Remete, László
2015
Calculating “small” solutions of relative Thue equations. Zbl 1390.11067
Gaál, István
2015
Binomial Thue equations and power integral bases in pure quartic fields. Zbl 1295.11120
Gaál, István; Remete, László
2014
Relative power integral bases in infinite families of quartic extensions of quadratic fields. Zbl 1335.11094
Gaál, István; Szabó, Tímea
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
2013
Power integral bases in parametric families of biquadratic fields. Zbl 1345.11074
Gaál, István; Szabó, Tímea
2012
A note on the minimal indices of pure cubic fields. Zbl 1220.11135
Gaál, István; Szabó, Tímea
2010
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
2010
Diophantine equations over global function fields. III: An application to resultant form equations. Zbl 1233.11036
Gaál, István; Pohst, Michael
2008
Solving resultant form equations over number fields. Zbl 1214.11042
Gaál, István; Pohst, Michael
2008
Diophantine equations over global function fields. I: The Thue equation. Zbl 1157.11011
Gaál, István; Pohst, Michael
2006
Diophantine equations over global function fields. II: $$R$$-integral solutions of Thue equations. Zbl 1142.11019
Gaál, István; Pohst, Michael
2006
Power integral bases in prime-power cyclotomic fields. Zbl 1193.11100
Gaál, István; Robertson, Leanne
2006
Index form equations in biquadratic fields: the $$p$$-adic case. Zbl 1111.11062
Gaál, István; Nyul, Gábor
2006
A fast algorithm for finding small solutions of $$F(x,y)=G(x,y)$$ over number fields. Zbl 1072.11095
Gaál, I.
2005
Index form equations in sextic fields: a hard computation. Zbl 1064.11084
Bilu, Yuri; Gaál, István; Győry, Kálmán
2004
A remark on prime divisors of lengths of sides of Heron triangles. Zbl 1096.11011
Gaál, István; Járási, István; Luca, Florian
2003
Recent results on power integral bases of composite fields. Zbl 1101.11012
Gaál, I.; Olajos, P.
2003
Diophantine equations and power integral bases. New computational methods. Zbl 1016.11059
Gaál, István
2002
On the resolution of relative Thue equations. Zbl 0985.11070
Gaál, István; Pohst, Michael
2002
Power integral bases in orders of composite fields. Zbl 1020.11064
Gaál, István; Olajos, Péter; Pohst, Michael
2002
On the resolution of resultant type equations. Zbl 1015.11010
Gaál, István
2002
Power integral bases in cubic relative extensions. Zbl 1014.11080
Gaál, István
2001
Computing power integral bases in quartic relative extensions. Zbl 0993.11055
Gaál, István; Pohst, Michael
2000
Solving index form equations in fields of degree 9 with cubic subfields. Zbl 0983.11077
Gaál, István
2000
A parametric family of quintic Thue equations. II. Zbl 0995.11024
Gaál, István; Lettl, Günter
2000
A parametric family of quintic Thue equations. Zbl 0983.11014
Gaál, István; Lettl, Günter
2000
Computing power integral bases in algebraic number fields. II. Zbl 1011.11068
Gaál, István
2000
Index form equations in quintic fields. Zbl 0930.11091
Gaál, István; Győry, Kálmán
1999
Power integer bases in algebraic number fields. Zbl 0936.11072
Gaál, István
1999
Power integral bases in composites of number fields. Zbl 0951.11012
Gaál, István
1998
Computing power integral bases in algebraic number fields. Zbl 1011.11067
Gaál, István
1998
Power integral bases in a parametric family of totally real cyclic quintics. Zbl 0899.11064
Gaál, István; Pohst, Michael
1997
Computing all power integral bases in orders of totally real cyclic sextic number fields. Zbl 0857.11069
Gaál, István
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
1996
On the resolution of index form equations in sextic fields with an imaginary quadratic subfield. Zbl 0873.11025
Gaál, István; Pohst, Michael
1996
Application of Thue equations to computing power integral bases in algebraic number fields. Zbl 0891.11062
Gaál, István
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
1995
Computing elements of given index in totally complex cyclic sextic fields. Zbl 0857.11068
Gaál, István
1995
On the resolution of index form equations in dihedral quartic number fields. Zbl 0823.11074
Gaál, István; Pethö, Attila; Pohst, Michael
1994
On the resolution of index form equations in quartic number fields. Zbl 0808.11023
Gaál, István; Pethö, Attila; Pohst, Michael
1993
Power integral bases in orders of families of quartic fields. Zbl 0814.11051
Gaál, István
1993
A fast algorithm for finding “small” solutions of $$F(x,y)= G(x,y)$$ over imaginary quadratic fields. Zbl 0806.11018
Gaál, István
1993
On the resolution of $$F(x,y)=G(x,y)$$. Zbl 0789.11022
Gaál, István
1993
On the resolution of index form equations in biquadratic number fields. I. Zbl 0726.11022
Gaál, I.; Pethö, A.; Pohst, M.
1991
On the resolution of index form equations in biquadratic number fields. II. Zbl 0726.11023
Gaál, I.; Pethö, A.; Pohst, M.
1991
On the indices of biquadratic number fields having Galois group $$V_ 4$$. Zbl 0724.11049
Gaál, I.; Pethö, A.; Pohst, M.
1991
On the resolution of some diophantine equations. Zbl 0733.11054
Gaál, I.
1991
On the resolution of index form equations. Zbl 0925.11053
Gaál, I.; Pethö, A.; Pohst, M.
1991
Computing all power integral bases of cubic fields. Zbl 0677.10013
Gaál, I.; Schulte, N.
1989
On the numbers of solutions of decomposable polynomial equations. Zbl 0655.10017
Evertse, J. H.; Gaál, I.; Györy, K.
1989
On the resolution of inhomogeneous norm form equations in two dominating variables. Zbl 0654.10020
Gaál, István
1988
Inhomogeneous discriminant form equations and integral elements with given discriminant over finitely generated integral domains. Zbl 0626.10015
Gaál, I.
1987
Inhomogeneous discriminant form and index form equations and their applications. Zbl 0632.10016
Gaál, I.
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.
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.
1984
all top 5

#### Cited by 97 Authors

 31 Gaál, István 14 Pohst, Michael E. 10 Pethő, Attila 7 Nakahara, Toru 6 Robertson, Leanne 6 Ziegler, Volker 5 Remete, László 4 Bennett, Michael A. 4 Heuberger, Clemens 4 Hoshi, Akinari 4 Spearman, Blair Kenneth 3 Jadrijević, Borka 3 Jones, Lenny K. 3 Nyul, Gábor 3 Smith, Hanson 2 Ahmad, Shahzad 2 Arnóczki, Tímea 2 Brunotte, Horst 2 Evertse, Jan-Hendrik 2 Fieker, Claus 2 Gassert, Thomas Alden 2 Ghadermarzi, Amir 2 Győry, Kálmán 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 Bérczes, Attila 1 Brindza, Béla 1 Chang, Mu-Ling 1 Cremona, John E. 1 Davis, Chad Tyler 1 Draziotis, Konstantinos A. 1 Dujella, Andrej 1 Garici, Tarek 1 Gras, Marie-Nicole 1 Hajdu, Lajos 1 Hameed, Abdul 1 Harrington, Joshua 1 He, Bo 1 Hu, Su 1 Husnine, Syed Muhammad 1 Huszti, Andrea 1 Jacobson, Michael John jun. 1 Jung, Ho Yun 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 Mignotte, Maurice 1 Miller-Sims, Laurel 1 Motoda, Yasuo 1 Nakano, Shin-ichi 1 Nguyen, Khoa Dang 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 Russell, Robin E. 1 Scheidler, Renate 1 Scholl, Travis 1 Shah, Kishor 1 Shin, Dong Hwa 1 Smart, Nigel P. 1 Stange, Katherine E. 1 Sultan, Mamoona 1 Surer, Paul 1 Szabó, Tímea 1 Tanoé, François E. 1 Uehara, Tsuyoshi 1 Wildanger, Klaus 1 Williams, Hugh Cowie 1 Wolske, Zack 1 Yang, Qiduan
all top 5

#### Cited in 32 Serials

 28 Journal of Number Theory 8 Mathematics of Computation 7 Journal de Théorie des Nombres de Bordeaux 7 International Journal of Number Theory 6 Acta Mathematica Hungarica 6 Journal of Symbolic Computation 5 Periodica Mathematica Hungarica 5 Experimental Mathematics 4 Rocky Mountain Journal of Mathematics 4 Functiones et Approximatio. Commentarii Mathematici 3 Acta Arithmetica 3 Acta Mathematica et Informatica Universitatis Ostraviensis 1 Bulletin of the Australian Mathematical Society 1 Journal of Mathematical Analysis and Applications 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Archiv der Mathematik 1 Compositio Mathematica 1 Czechoslovak Mathematical Journal 1 Manuscripta Mathematica 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 Mathematics 1 International Journal of Algebra and Computation 1 Elemente der Mathematik 1 Annales Mathématiques Blaise Pascal 1 Taiwanese Journal of Mathematics 1 LMS Journal of Computation and Mathematics 1 Journal of Algebra and its Applications 1 Journal of Mathematical Cryptology

#### Cited in 5 Fields

 108 Number theory (11-XX) 3 Field theory and polynomials (12-XX) 2 Algebraic geometry (14-XX) 2 Information and communication theory, circuits (94-XX) 1 Potential theory (31-XX)