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Riemann zeta function
Čoupek, Petr ; Rokyta, Mirko (advisor) ; Zahradník, Miloš (referee)
Riemann zeta function represents an important tool in analytical number theory with various applications in quantum mechanics, probability theory and statistics. First introduced by Bernhard Riemann in 1859, zeta function is a central object of many outstanding problems. From previous results follows the importance of zeta function for further development in the field of number theory. This thesis provides basic properties of the Riemann zeta function. In particular, we prove theorems concerning the distribution of its roots outside and inside the critical strip which leads to the formulation of the Riemann hypothesis and theorems concerning the irrationality of selected values of the Riemann zeta function including the proof of the irrationality of ζ(3). 1
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The declension of variation. On the notion of multiplicity in Gilles Deleuze
Bastidas Bolaños, David Antonio ; Goddard, Jean-Christophe (advisor) ; Sáez Tajafuerce, Begonya (referee)
The declension of variation. On the notion of multiplicity in Gilles Deleuze This paper aims at a reconstruction of the notion of multiplicity in the thought of the French philosopher Gilles Deleuze. To this end, our guiding thread corresponds to the relationship that this thinker establishes between the mathematical doctrine of Bernhard Riemann and the philosophy of Henri Bergson. Our purpose is to go through the various appearances of this relationship and to reconstruct the fundamental axes of an original concept of multiplicity that we believe Deleuze's thought holds. Thus, our inquiry, via a strategic journey through the Bergsonism, A Thousand Plateaus and Difference and Repetition, uncovers a double articulation for the deleuzian multiplicity. This double articulation is expressed in the two axes of thematization that we develop, namely coherence and inherence, or in other terms, a multidimensional organization and an activity of internal division. From these two axes, we believe, the notion of multiplicity describes the dynamics proper to a mouvement of continuous change or variation of nature. Keywords : Deleuze, Multiplicity, Variation, Bergson, Riemann, Bergsonism, A Thousand Plateaus, Difference and repetition.
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Riemann zeta function
Čoupek, Petr ; Rokyta, Mirko (advisor) ; Zahradník, Miloš (referee)
Riemann zeta function represents an important tool in analytical number theory with various applications in quantum mechanics, probability theory and statistics. First introduced by Bernhard Riemann in 1859, zeta function is a central object of many outstanding problems. From previous results follows the importance of zeta function for further development in the field of number theory. This thesis provides basic properties of the Riemann zeta function. In particular, we prove theorems concerning the distribution of its roots outside and inside the critical strip which leads to the formulation of the Riemann hypothesis and theorems concerning the irrationality of selected values of the Riemann zeta function including the proof of the irrationality of ζ(3). 1
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