Masteruppsatser

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Browsing Masteruppsatser by Author "Elofsson, Carl"

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    Prime number races
    (2024-08-12) Elofsson, Carl; University of Gothenburg/Department of Mathematical Science; Göteborgs universitet/Institutionen för matematiska vetenskaper
    In this thesis we investigate the behaviour of primes in arithmetic progressions, with a focus on the phenomenon known as Chebyshev’s bias. Under the assumption of the Generalized Riemann Hypothesis and the Linear Independence Hypothesis, we prove that there is a bias towards quadratic non-residues. Additionally we extend the investigation to the setting of function fields. In the function field setting, we investigate the behaviour of prime polynomials in residue classes modulo a fixed monic polynomial. Moreover, we prove that for an irreducible polynomial m there is a bias towards quadratic non-residues modulo m.