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    • Diophantine Equations in Many Variables 

      Dumke, Jan Henrik (2014-11-06)
      Let K denote a p-adic field and $F_1,..,F_r \in k[x_1, . . . , x_n]$ be forms with respective degrees $d_1, . . . , d_r$. A contemporary version of a conjecture attributed to E. Artin states that $F_1, . . . , F_r$ have a ...
    • Diophantine Representation in Thin Sequences 

      Baur, Stefan (2016-08-24)
      In this work we investigate conditions under which forms of arbitrary degree represent almost all elements of thin sequences (especially the set of squares). Stronger results are given for forms of degree 3 and 4.
    • Quadratische Diophantische Gleichungen über algebraischen Zahlkörpern 

      Helfrich, Lutz (2015-04-23)
      A search bound for the smallest solution of a quadratic diophantine equation over number fields in at least three variables is established.
    • The Barban-Davenport-Halberstam for tuples of k-free numbers 

      Parry, Tomos (2020-10-23)
      An asymptotic formula for variance of tuples of k-free numbers in arithmetic progressions
    • The distribution of rational points on some projective varieties 

      Dehnert, Fabian (2020-01-09)
      This thesis is concerned with establishing Manin's conjecture on the distribution of ratinal points for a certain class of bihomogeneous varieties. It generalizes work of Vaughan on the representation of integers as sum ...
    • Two Cases of Artin's Conjecture 

      Kaesberg, Miriam Sophie (2021-02-25)
      Let $f_1, \dots, f_R$ be forms of degree $k_1, \dots, k_R$ in $s$ variables. A generalised version of a conjecture by Artin states that the equations $f_1= \dots=f_R=0$ have a non-trivial $p$-adic solution for all primes ...