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	Arithmetic-geometric mean sequences and elliptic curves over finite fields Bátorová, Natália ; Kala, Vítězslav (advisor) ; Tinková, Magdaléna (referee) In the thesis we introduce arithmetic geometric mean sequences, firstly over real num- bers and then over finite fields Fq such that q ≡ 3 (mod 4). We connect the sequences with graphs and prove some properties over general finite fields for these graphs. We also extend arithmetic geometric mean sequences over Fq such that q ≡ 5 (mod 8) and we show a connection between elliptic curves and arithmetic geometric mean sequences over Fq such that q ≡ 3 (mod 4). Detailed record
	Arithmetics of number fields and generalized continued fractions Tinková, Magdaléna ; Kala, Vítězslav (advisor) ; Blomer, Valentin (referee) ; Earnest, Andrew (referee) This thesis focuses on additively indecomposable integers in totally real number fields and their application in the study of universal quadratic forms. For the determination of such elements, we develop two different methods, which are based on their geometrical properties and multidimensional continued fractions, especially on the so-called Jacobi- Perron algorithm. In particular, we are interested in quadratic, biquadratic, and cubic number fields. For them, we provide several new results on the number of variables of their universal quadratic forms and the structure, norms, and minimal traces of their indecomposable integers. One part is also devoted to the related question of the so-called Pythagoras number, where we use our results on indecomposable integers. 1 Detailed record
	Visibly irreducible polynomials Bžatková, Kateřina ; Kala, Vítězslav (advisor) ; Tinková, Magdaléna (referee) Thesis is focused on the irreducibility of polynomials over finite fields. Paper Evan M. O'Dorney, Visibly irreducible polynomials over finite fields, when prooving irreducibility uses visibly irreducible decomposition VID, which is type of decomposition easily determinating irreducibility. In the thesis we analyse in detail results from this paper. Furthermore we generalize the definition of VID from mentioned paper by omitting a condition on any degree of polynomials. Detailed record

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2	Tinková, Marie

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