Tudóstér: Gaál István publikációi

El Fadil, L., Gaál, I.: Integral Bases and Monogenity of Pure Number Fields with Non-Square Free Parameters up to Degree 9.
Biophysical Journal. 83 (1), 61-86, 2023.

Gaál, I.: Monogenity in totally real extensions of imaginary quadratic fields with an application to simplest quartic fields.
Acta Sci. Math. 89 (1-2), 3-12, 2023.

Gaál, I., Remete, L.: On the monogenity of pure quartic relative extensions of Q(i).
Acta Sci. Math. 2023 1-15, 2023.

Gaál, I., Pohst, M.: On calculating the number N(D) of global cubic fields F of given discriminant D.
J. Number Theory. 236 479-491, 2022.

Gaál, I.: On the monogenity of certain binomial compositions.
J. Algebra, Number Theory & Appl. 57 1-16, 2022.

Gaál, I.: An experiment on the monogenity of a family of trinomials.
J. Algebra, Number Theory & Appl. 51 (1), 97-111, 2021.

Gaál, I.: Calculating "small" solutions of inhomogeneous relative Thue inequalities.
Funct. Approx. Comment. Math. 65 (2), 141-156, 2021.

Gaál, I., Pohst, M., Pohst, M.: On computing integral points of a Mordell curve - the method of Wildanger revisited.
Exp. Math. 30 (1), 127-134, 2021.

Gaál, I.: Monogenity in totally complex sextic fields, revisited.
J. Algebra, Number Theory & Appl. 47 (1), 87-98, 2020.

Gaál, I., Jadrijević, B., Remete, L.: Totally real Thue inequalities over imaginary quadratic fields: an improvement.
Glas. Mat. 55 (2), 191-194, 2020.

Gaál, I.: Calculating relative power integral bases in totally complex quartic extensions of totally real fields.
J. Algebra, Number Theory & Appl. 44 (2), 129-157, 2019.

Gaál, I.: Diophantine Equations and Power Integral Bases.
Birkhäuser, Basel, 326 p., 2019. ISBN: 9783030238643

Gaál, I., Remete, L.: Integral Bases and Monogenity of Composite Fields.
Exp. Math. 28 (2), 209-222, 2019.

Gaál, I., Remete, L.: Power integral bases in cubic and quartic extensions of real quadratic fields.
Acta Sci. Math. 85 (3-4), 413-429, 2019.

Gaál, I., Jadrijević, B., Remete, L.: Simplest quartic and simplest sextic Thue equations over imaginary quadratic fields.
Int. J. Number Theory. 15 (1), 11-27, 2019.

Gaál, I., Remete, L.: Integral bases and monogenity of the simplest sextic fields.
Acta Arith. 183 (2), 173-183, 2018.

Gaál, I., Jadrijević, B., Remete, L.: Totally real Thue inequalities over imaginary quadratic fields.
Glas. Mat. 53 (2), 229-238, 2018.

Gaál, I., Remete, L.: Integral bases and monogenity of pure fields.
J. Number Theory. 173 129-146, 2017.

Gaál, I., Remete, L.: Non-monogenity in a family of octic fields.
Rocky Mt. J. Math. 47 (3), 817-824, 2017.

Gaál, I., Remete, L., Szabó, T.: Calculating power integral bases by using relative power integral bases.
Funct. Approx. Comment. Math. 54 (2), 141-149, 2016.

Gaál, I.: Calculating "small" solutions of relative Thue equations.
Exp. Math. 24 (2), 142-149, 2015.

Gál, Z., Gaál, I.: Debreceni szuperszámítógép szolgáltatások a kutatásban.
In: Az elmélet és a gyakorlat találkozása a térinformatikában = Theory meets practice in GIS : Térinformatikai Konferencia és Szakkiállítás, Debreceni Egyetem / [szerk. Boda Judit], Debreceni Egyetemi Kiadó, Debrecen, 145-153, 2015. ISBN: 9789633184882

Gaál, I., Remete, L.: Power integral bases in a family of sextic fields with quadratic subfields.
Tatra Mt. Math. Publ. 64 (1), 59-66, 2015.

Gaál, I., Remete, L.: Solving binomial Thue equations.
J. Algebra, Number Theory & Appl. 36 (1), 29-42, 2015.

Gaál, I., Remete, L.: Binomial Thue equations and power integral bases in pure quartic fields.
J. Algebra, Number Theory & Appl. 32 (1), 49-61, 2014.

Gaál, I., Petrányi, G.: Calculating all elements of minimal index in the infinite parametric family of simplest quartic fields.
Czech. Math. J. 64 (2), 465-475, 2014.

Gaál, I., Remete, L., Szabó, T.: Calculating power integral bases by solving relative Thue equations.
Tatra Mt. Math. Publ. 59 (1), 79-92, 2014.

Gaál, I., Kozma, L.: Lineáris algebra.
Debreceni Egyetemi Kiadó, Debrecen, 167 p., 2013. ISBN: 9789633183229

Fieker, C., Gaál, I., Pohst, M.: On computing integral points of a Mordell curve over rational function fields in characteristic >3.
J. Number Theory. 133 (2), 738-750, 2013.

Gaál, I., Szabó, T.: Relative power integral bases in infinite families of quartic extensions of quadratic field.
JP J. Algebra, Number Theory Appl. 29 (1), 31-43, 2013.

Gaál, I., Pohst, M.: The sum of two S-units being a perfect power in global function fields.
Mathematica Slovaka. 63 (1), 69-76, 2013.

Gaál, I., Szabó, T.: Power integral bases in parametric families of biquadratic fields.
JP J. Algebra, Number Theory Appl. 24 (1), 105-114, 2012.

Gaál, I., Pohst, M.: Solving explicitly F(x,y)=G(x,y) over function fields.
Funct. Approx. Comment. Math. 45 (1), 79-88, 2011.

Gaál, I., Szabó, T.: A note on the minimal indices of pure cubic fields.
JP J. Algebra, Number Theory Appl. 19 (2), 129-139, 2010.

Gaál, I., Pohst, M.: Diophantine equations over global function fields IV: S-unit equations in several variables with an application to norm form equations.
J. Number Theory. 130 (3), 493-506, 2010.

Gaál, I., Pohst, M.: Diophantine equations over global function fields V: Resultant equations in two unknown polynomials.
Int. J. Pure Appl. Math. 53 307-317, 2009.

Gaál, I., Pohst, M.: On solving norm equations in global function fields.
J. Math. Crypt. 3 237-248, 2009.

Gaál, I., Pohst, M.: A note on the number of solutions of resultant equations.
J. Algebra, Number Theory and Applications. 12 185-189, 2008.

Gaál, I., Pohst, M.: Diophantine equations over global function fields III: An application to resultant form equations.
Funct. Approx. Comment. Math. 39 (1), 97-102, 2008.

Gaál, I., Pohst, M.: Solving resultant form equations over number fields.
Math. Comput. 77 (264), 2447-2453, 2008.

Gaál, I., Pohst, M.: Diophantine equations over global function fields I: The Thue equation.
J. Number Theory. 119 (1), 49-65, 2006.

Gaál, I., Pohst, M.: Diophantine Equations over Global Function Fields II: Integral Solutions of Thue Equations.
Exp. Math. 15 (1), 1-6, 2006.

Gaál, I., Nyul, G.: Index form equations in biquadratic fields: the p-adic case.
Publ. Math. Debrecen. 68 (1-2), 225-242, 2006.

Gaál, I., Robertson, L.: Power integral bases in prime-power cyclotomic fields.
J. Number Theory. 120 (2), 372-384, 2006.

Gaál, I.: Solving explicitly decomposable form equations over global function fields.
J. Algebra, Number Theory & Appl. 6 (2), 425-434, 2006.

Gaál, I.: A fast algorithm for finding small solutions of F(X,Y)=G(X,Y) over number fields.
Acta Math. Hung. 106 (1-2), 41-51, 2005.

Bilu, Y., Gaál, I., Győry, K.: Index form equations in sextic fields: a hard computation.
Acta Arith. 115 (1), 85-96, 2004.

Gaál, I., Járási, I., Luca, F.: A remark on prime divisors of lengths of sides of Heron triangles.
Exp. Math. 12 (3), 303-310, 2003.

Gaál, I., Olajos, P.: Recent results on power integral bases of composite fields.
Acta Acad. Paed. Agr. Sect. Math. 30 45-54, 2003.

Gaál, I.: Diophantine Equations and Power Integral Bases.
Birkhauser Boston, Boston; Basel; Berlin, 184 p., 2002. ISBN: 9780817642716

Gaál, I., Pohst, M.: On the resolution of relative Thue equations.
Math. Comput. 71 (237), 429-440, 2002.

Gaál, I.: On the resolution of resultant type equations.
J. Symb. Comp. 34 (2), 137-144, 2002.

Everest, G., Gaál, I., Győry, K., Röttger, C.: On the spatial distribution of solutions of decomposable form equations.
Math. Comput. 71 (238), 633-648, 2002.

Gaál, I., Olajos, P., Pohst, M.: Power integral bases in orders of composite fields.
Exp. Math. 11 (1), 87-90, 2002.

Gaál, I., Nyul, G.: Computing all monogeneous mixed dihedral quartic extensions of a quadratic field.
J. Theor. Nr. Bordx. 13 (1), 137-142, 2001.

Gaál, I.: Power integral bases in cubic relative extensions.
Exp. Math. 10 (1), 133-139, 2001.

Gaál, I.: An efficient algorithm for the explicit resolution of norm form equations.
Publ. Math. Debr. 56 (3-4), 375-390, 2000.

Gaál, I., Lettl, G.: A parametric family of quintic Thue equations II..
Monatsh. Math. 131 (1), 29-35, 2000.

Gaál, I.: Computing power integral bases in algebraic number fields II.
In: Algebraic number theory and Diophantine analysis: proceedings of the international conference held in Graz, Austria, August 30 to September 5, 1998.. Ed.: F. Halter-Koch, Robert F. Tichy, De Gruyter, Berlin, 153-161, 2000. ISBN: 3110163047

Gaál, I., Pohst, M.: Computing Power Integral Bases in Quartic Relative Extensions.
J. Number Theory. 85 (2), 201-219, 2000.

Gaál, I., Kozma, L.: Lineáris algebra.
Kossuth Egyetemi Kiadó, Debrecen, 163 p., 2000.

Gaál, I.: Solving index form equations in fields of degree nine with cubic subfields.
J. Symb. Comp. 30 (2), 181-193, 2000.

Gaál, I., Győry, K.: Index form equations in quintic fields.
Acta Arith. 89 (4), 379-396, 1999.

Gaál, I.: Power integral bases in algebraic number fields.
Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Comput. 18 61-87, 1999.

Gaál, I.: Computing power integral bases in algebraic number fields.
In: Number theory : diophantine, computational, and algebraic aspects : proceedings of the international conference held in Eger, Hungary, July 29-August 2, 1996 / editors, Kálmán Györy, Attila Pethö, Vera T. Sós, Walter de Gruyter, Berlin ; New York, 243-254, 1998.

Gaál, I., Kozma, L.: Lineáris algebra.
Kossuth Egyetemi Kiadó, Debrecen, 163 p., 1998.

Gaál, I.: Power integral bases in composits of number fields.
Can. math. bull. 41 158-161, 1998.

Gaál, I., Kozma, L.: Lineáris algebra és geometria.
Kossuth Lajos Tudományegyetem Matematikai és Informatikai Intézet, [Debrecen], 196 p. ;, 1997.

Gaál, I., Pohst, M.: Power integral bases in a parametric family of totally real cyclic quintics.
Math. Comp. 66 (220), 1689-1696, 1997.

Gaál, I.: Algorithms for the computation of power integral bases in algebraic number fields.
In: International Symposium on Symbolic and Algebraic Computations

Gaál, I.: Application of Thue equations to computing power integral bases in algebraic number fields.
In: Algorithmic Number Theory : Proc. Conf. ANTS II, Talence, France, 1996. Ed.: Henri Cohen, Springer, Berlin, 151-155, 1996, (Lecture notes in computer science ; 1122)

Gaál, I.: Computing all power integral bases in orders of totally real cyclic sextic number fields.
Math. Comp. 65 801-822, 1996.

Gaál, I., Kozma, L.: Lineáris algebra és geometria I..
Kossuth Lajos Tudományegyetem Matematikai és Informatikai Intézet, Debrecen, 139 p., 1996.

Gaál, I., Pohst, M.: On the resolution of index form equations in sextic fields with an imaginary quadratic subfield.
J. Symbolic. Comput. 22 (4), 425-434, 1996.

Gaál, I., Pethő, A., Pohst, M.: Simultaneous representation of integers by a pair of ternary quadratic forms: with an application to index form equations in quartic number fields.
J. Number Theory. 57 (1), 90-104, 1996.

Gaál, I.: Computing elements of given index in totally cyclic sextie fields.
J. Symb. Comp. 20 61-69, 1995.

Gaál, I., Pethő, A., Pohst, M.: On the resolution of index form equations in biquadratic number-fields III.: the bicyclic biquadratic case.
J. Number Theory. 53 (1), 100-114, 1995.

Gaál, I., Pethő, A., Pohst, M.: On the resolution of index form equations in dihedral quartic number fields.
Exp. Math. 3 245-254, 1994.

Gaál, I., Pethő, A., Pohst, M.: On the resolution of index form equations in dihedral quartic number fields IV..
Exp. Math. 3 (3), 245-254, 1994.

Gaál, I.: A fast alogrithm for finding "small" solutions of F(x,y)=G(x,y) over imaginary quadratic fields.
J. Symb. Comp. 16 321-328, 1993.

Gaál, I.: On the resolution of F(x,y)=G(x,y).
J. Symb. Comp. 16 295-303, 1993.

Gaál, I., Pethő, A., Pohst, M.: On the resolution of index form equations in quartic number fields.
J. Symb. Comp. 16 (6), 563-584, 1993.

Gaál, I.: Power integral bases in orders of families of quartic fields.
Publ. Math.-Debr. 42 253-263, 1993.

Gaál, I., Pethő, A., Pohst, M.: On the indices of biquadratic number fields having Galois group V4.
Arch. Math. 57 (4), 357-361, 1991.

Pohst, M., Gaál, I., Pethő, A.: On the resolution of index form equations.
In: Proceedings of the 1991 International Symposium on Symbolic and Algebraic Computation: ISSAC '91. Bonn, Németország, 1991.07.15-1991.07.17.. Szerk.: Watt, S. M, ACM Press, New York, 185-186, 1991.

Gaál, I., Pethő, A., Pohst, M.: On the resolution of index form equations in biquadratic number fields I..
J. Number Theory. 38 (1), 18-34, 1991.

Gaál, I., Pethő, A., Pohst, M.: On the resolution of index form equations in biquadratic number fields II..
J. Number Theory. 38 (1), 35-51, 1991.

Gaál, I.: On the computer resolution of index form equations.
In: Proceedings of the Regional Mathematical Conference, Kalsk, September 1988. : Section, algebra and number theory / editor Aleksander Grytczuk, Pedagogical University of Zielona Góra, Zielona Góra, 21-27, 1990.

Schulte, N., Gaál, I.: Computing all power integral bases of Cubic fields..
Math. Comp. 53 689-696, 1989.

Evertse, J., Gaál, I., Győry, K.: On the numbers of solutions of decomposable polynomial equations.
Arch. Math. 52 (4), 337-353, 1989.

Gaál, I.: Inhomogeneous norm form equations over function fields.
Acta Arith. 51 (1), 61-73, 1988.

Gaál, I.: Integral elements with given discriminant over function fields.
Acta Math. Hung. 52 (1-2), 133-146, 1988.

Gaál, I.: On the resolution of inhomogeneous norm form equations in two dominating variables.
Math. Comp. 51 359-373, 1988.

Gaál, I.: Inhomogeneous discriminant form equations and integral elements with given discriminant over finitely generated integral domains.
Publ. Math.-Debr. 34 109-122, 1987.

Gaál, I., Brindza, B.: Inhomogeneous norm form equations in two dominating variables over function fields.
Publ. Math.-Debr. 50 147-153, 1987.

Gaál, I.: Inhomogeneous discriminant form and index form equations and their applications.
Publ. Math.-Debr. 33 21-27, 1986.

Gaál, I.: Inhomogenous discriminant form and index form equations anf their applications.
Publ. Math.-Debr. 33 21-27, 1986.

Gaál, I.: Norm form equations with several dominating variables and explicit lower bounds for inhomogeneous linear forms with algebraic coefficients, II.
Stud. Sci. Math. Hung. 20 (1-4), 333-344, 1985.

Gaál, I.: Norm form equations with several dominating variables and explicit lower bounds for inhomogeneous linear forms with algebraic coefficients.
Stud. Sci. Math. Hung. 19 (2-4), 399-411, 1984.