List of publications

István Gaál

 

[1] I.Gaál, Norm form equations with several dominating variables and explicit lower bounds for inhomogeneous linear forms with algebraic coefficients, Studia Sci. Math. Hungar., 19 (1984), 399--411.

[2] I.Gaál, Norm form equations with several dominating variables and explicit lower bounds for inhomogeneous linear forms with algebraic coefficients, II., Studia Sci. Math. Hungar., 20 (1985), 333--344

[3] I.Gaál, Inhomogeneous discriminant form and index form equations and their applications,Publ. Math.(Debrecen), 33 (1986), 21--27.

[4] I.Gaál, Integral elements with given discriminant, XVI. Steiermärkisch Mathematischen Symposium, Bericht Nr. 272, (1986), 1--12.

[5] I.Gaál, Inhomogeneous discriminant form equations and integral elements with given discriminant over finitely generated integral domains, Publ. Math. (Debrecen), 34 (1987), 109--122.

[6] B.Brindza and I.Gaál, Inhomogeneous norm form equations in two dominating variables over function fields, Acta Math. Hungar., 50 (1987), 147--153.

[7] I.Gaál, Inhomogeneous decomposable form equations and their applications (in Hungarian), University doctor thesis, Kossuth Lajos University, 1987.

[8] I.Gaál, Integral elements with given discriminant over function fields, Acta Math. Hungar., 52 (1988), 133--146.

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

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

[11] I.Gaál, Decomposable polynomial equations and their applications (in Hungarian), Candidate (Ph.D.) thesis, Kossuth Lajos University, 1989.

[12] J.H.Evertse, I.Gaál and K.Györy, On the number of solutions of decomposable polynomial equations, Archiv der Math., 52 (1989), 337--353.

[13] I.Gaál and N.Schulte, Computing all power integral bases of cubic fields, Math. Comp., 53 (1989), 689--696.

[14] I.Gaál, On the computer resolution of index form equations, in "Algebra and Number Theory", ed. by A.Grytzuk, Pedagogical University, Zielona G\'ora, 1990, pp.21--27.

[15] I.Gaál, A.Pethö and M.Pohst, On the resolution of index form equations in biquadratic number fields, I, J.Number Theory, 38,(1991), 18--34.

[16] I.Gaál, A.Pethö and M.Pohst, On the resolution of index form equations in biquadratic number fields, II, J.Number Theory, 38,(1991), 35--51.

[17] I.Gaál, On the resolution of some diophantine equations, in "Computational Number Theory", ed. by A.Pethö, M.E.Pohst, H.C.Williams and H.G.Zimmer, Walter de Gruyter, Berlin--New York 1991, pp.261--280.

[18] I.Gaál, A.Pethö and M.Pohst, On the indices of biquadratic number fields having Galois group $V_4$ , Archiv der Math., 57 (1991), 357--361.

[19] I.Gaál, A.Pethö and M.Pohst, On the resolution of index form equations, Proc. of the 1991 International Symposium on Symbolic and Algebraic Computation, ed. by Stephen M. Watt, ACM Press, 1991, pp. 185-186.

[20] I.Gaál, On the resolution of $F(x,y)=G(x,y)$,J.Symbolic Computation, 16(1993), 295--303.

[21] I.Gaál, Power integral bases in orders of families of quartic fields, Publ.Math. (Debrecen), 42(1993), 253--263.

[22] I.Gaál, A fast algorithm for finding "small" solutions of F(x,y)=G(x,y)over imaginary quadratic fields, J.Symbolic Computation,16(1993), 321--328.

[23] I.Gaál, A.Pethö and M.Pohst, On the resolution of index form equations in biquadratic number fields, III. The bicyclic biquadratic case, J.Number Theory, 53(1995), 100--114.

[24] I.Gaál, A.Pethö and M.Pohst, On the resolution of index form equations in quartic number fields, J.Symbolic Computation, 16(1993), 563--584.

[25] I.Gaál, A.Pethö and M.Pohst, On the resolution of index form equations in dihedral quartic number fields, J. Experimental Math., 3(1994), 245--254.

[26] I.Gaál, A.Pethö and M.Pohst, 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(1996), 90--104.

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

[28] I.Gaál, Computing elements of given index in totally complex cyclic sextic number fields, J.Symbolic Comp., 20(1995), 61--69.

[29] I.Gaál, Power integral bases in algebraic number fields, Ann. Univ. Sci. Budapestiensis R. Eötvös Nom., Sect. Computatorica, 18(1999), 61--87.

[30] I.Gaál and M.Pohst, On the resolution of index form equations in sextic fields with an imaginary quadratic subfield, J.Symbolic Comp, 22 (1996), 425--434.

[31] I.Gaál, Application of Thue equations to computing power integral bases in algebraic number fields, Proc. Conf. ANTS II, Talence, France, 1996. Lecture Notes in Computer Science 1122, Springer 1996, pp. 151--155.

[32] I.Gaál, Algorithms for the computation of power integral bases in algebraic number fields, ISSAC'96 Poster Session Abstracts, Zürich, pp. 29--32.

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

[34] I.Gaál, Power integral bases in composits of number fields, Canad. Math. Bull., 41(1998), 158--161.

[35] I.Gaál, Computing power integral bases in algebraic number fields, Proc. Conf. Number Theory Eger, Hungary, 1996. In: Number Theory, Walter de Gruyter, 1998, pp. 243--254.

[36] I.Gaál, Solving index form equations in fields of degree nine with cubic subfields, J.Symbolic Comput., 30(2000), 181-193.

[37] I.Gaál and G.Lettl, A parametric family of quintic Thue equations, Math. Comput., 69(1999), 851-859.

[38] I.Gaál, Power integral bases in cubic relative extensions, Experimental Math., 10(2001), 133-139.

[39] I.Gaál and M.Pohst, On the resolution of relative Thue equations, Math. Comp., 71(2002), 429-440.

[40] I.Gaál and K.Györy, Index form equations in quintic fields, Acta Arithm., 89(1999), 379--396.

[41] I.Gaál and M.Pohst, Computing power integral bases in quartic  relative extensions, J.Number Theory, 85(2000), 201-219.

[42] I.Gaál, An efficient algorithm for the explicit resolution of norm form equations, Publ. Math. (Debrecen), 56(2000), 375-390.

[43] I.Gaál, Computing power integral bases in algebraic number fields II, Algebraic number theory and diophantine analysis, Proc. Conf. Graz, 1998, ed. F.Halter-Koch and R.F.Tichy, Walter de Gruyter, 2000, pp. 153-161.

[44] I.Gaál and G.Nyul, Computing all monogeneous dihedral quartic extensions of a quadratic field, J.Theorie Nombres Bordeaux, 13(2001), 137-142.

[45] I.Gaál and G.Lettl, A parametric family of quintic Thue equations II., Monatsh. Math., 131(2000), 29-35.

[46] G.Everest, I.Gaál, K.Győry and C.R.Röttger, On the spatial distribution of solutions of decomposable form equations, Math. Comp., 71(2002), 633-648.

[47] I.Gaál, M.Pohst and P.Olajos, Power integral bases in orders of composits of number fields, Experimental Math., 11(2002), 87-90.

[48] I.Gaál, Constructive methods for solving diophantine equations, Academic Doctor’s Thesis, 2001.

[49] I.Gaál, Diophantine Equations and Power Integral Bases, New Computational Methods, Birkhauser Boston, 2002.

[50] I.Gaál, On the resolution of resultant type equations, J.Symbolic Comput., 34(2002), 137-144.

[51] I.Gaál, I.Járási and F.Luca, A remark on prime divisors of lengths of sides of Heron triangles, Experimental Math., 12(2003), 303--310.

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

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

[54] I.Gaál and P.Olajos, Recent results on power integral bases of composite fields, Acta Acad. Paed. Agriensis, Sect. Math.,  30(2003), 45--54.

[55] Y.Bilu, I.Gaál and K.Győry, Index form equations in sextic fields: a hard computation, Acta Arithm., 115.1 (2004), 85-96.

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

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

[58] I.Gaál and M.Pohst, Diophantine equations over global function fields II: S-integral solutions of Thue equations, Experimental Mathematics, 15(2006), 1-6.

[59] I.Gaál, Solving explicitely decomposable form equations over global function fields, JP Journal of Algebra, Number Theory and Appl. 6(2006), 425 - 434.

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

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

[62] I.Gaál and M.Pohst, Solving resultant form equations over number fields, Math Comput., 77(2008), 2447--2453.

[63] I.Gaál and M.Pohst, A note on the number of solutions of resultant equations, JP Journal of Algebra, Number Theory and Applications, 12(2008), 185 - 189.

[64] I.Gaál and M.Pohst, Diophantine equations over global function fields V: Resultant equations in two unknown polynomials, Int. J. Pure Appl. Math. 53(2009), No. 3., 307--317.

[65] I.Gaál and M.Pohst, On solving norm equations in global function fields, J. Math. Crypt., 3(2009), 237--248.

[66] I.Gaál and M.Pohst, Solving explicitly diophantine equations of type F(x,y)=G(x,y) over function fields, Functiones et Approximatio, 45.1(2011), 79--88. 

[67] I.Gaál and M.Pohst, The sum of two S-units being a perfect power in global function fields, Math. Slovaka, 63(2013), 69--76.

[68] I.Gaál and T. Szabó, A note on the minimal indices of pure cubic fields, JP Journal of Algebra, Number Theory and Applications, 19(2010), 129 - 139

[69] I.Gaál and T. Szabó, Power integral bases in parametric families of biquadratic fields, JP Journal of Algebra, Number Theory and Applications, 21(2012), 105--114.

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

[71] I.Gaál and G.Petrányi,  Calculating all elements of minimal index in the infinite parametric family of simplest quartic fields, Czech. Math. Journal, 64(139)(2014), 465–475.

[72] I.Gaál and T.Szabó, Relative power integral bases in infinite families of quartic extensions of quadratic field, JP Journal of Algebra, Number Theory and Applications,  29(2013), 31--43.

[73] I.Gaál and L.Remete, Binomial Thue equations and power integral bases in pure quartic fields, JP Journal of Algebra, Number Theory and Applications, 32(2014), 49--61.

[74] I.Gaál, Calculating "small" solutions of relative Thue equations, Experimantal Math. to appear.

[75] I.Gaál and L.Remete, Solving binomial Thue equations, JP Journal of Algebra, Number Theory and Applications, to appear.

[76] I.Gaál, L.Remete and T.Szabó, Calculating power integral bases by solving relative Thue equations, Tatra Mt. Math. Publ. to appear.