@article{34841,
  abstract     = {{We give an exact formula for the number of G-extensions of local function fields Fq((t)) for finite abelian groups G up to a conductor bound. As an application we give a lower bound for the corresponding counting problem by discriminant.
}},
  author       = {{Klüners, Jürgen and Müller, Raphael}},
  issn         = {{0022-314X}},
  journal      = {{Journal of Number Theory}},
  keywords     = {{Algebra and Number Theory}},
  pages        = {{311--322}},
  publisher    = {{Elsevier BV}},
  title        = {{{The conductor density of local function fields with abelian Galois group}}},
  doi          = {{10.1016/j.jnt.2019.11.007}},
  volume       = {{212}},
  year         = {{2020}},
}

@article{34916,
  abstract     = {{We describe the powers of irreducible polynomials occurring as characteristic polynomials of automorphisms of even unimodular lattices over number fields. This generalizes results of Gross & McMullen and Bayer-Fluckiger & Taelman.}},
  author       = {{Kirschmer, Markus}},
  issn         = {{0022-314X}},
  journal      = {{Journal of Number Theory}},
  keywords     = {{Algebra and Number Theory}},
  pages        = {{121--134}},
  publisher    = {{Elsevier BV}},
  title        = {{{Automorphisms of even unimodular lattices over number fields}}},
  doi          = {{10.1016/j.jnt.2018.08.004}},
  volume       = {{197}},
  year         = {{2019}},
}

@article{34844,
  abstract     = {{Let k be a number field, K/k a finite Galois extension with Galois group G, χ a faithful character of G. We prove that the Artin L-function L(s,χ,K/k) determines the Galois closure of K over $\ℚ$. In the special case $k=\ℚ$ it also determines the character χ. }},
  author       = {{Klüners, Jürgen and Nicolae, Florin}},
  issn         = {{0022-314X}},
  journal      = {{Journal of Number Theory}},
  keywords     = {{Algebra and Number Theory}},
  pages        = {{161--168}},
  publisher    = {{Elsevier BV}},
  title        = {{{Are number fields determined by Artin L-functions?}}},
  doi          = {{10.1016/j.jnt.2016.03.023}},
  volume       = {{167}},
  year         = {{2016}},
}

@article{42792,
  abstract     = {{We enumerate all positive definite ternary quadratic forms over number fields with class number at most 2. This is done by constructing all definite quaternion orders of type number at most 2 over number fields. Finally, we list all definite quaternion orders of ideal class number 1 or 2.}},
  author       = {{Kirschmer, Markus and Lorch, David}},
  issn         = {{0022-314X}},
  journal      = {{Journal of Number Theory}},
  keywords     = {{Algebra and Number Theory}},
  pages        = {{343--361}},
  publisher    = {{Elsevier BV}},
  title        = {{{Ternary quadratic forms over number fields with small class number}}},
  doi          = {{10.1016/j.jnt.2014.11.001}},
  volume       = {{161}},
  year         = {{2016}},
}

@article{42793,
  abstract     = {{Suppose Q is a definite quadratic form on a vector space V over some totally real field K ≠ Q. Then the maximal integral Zₖ-lattices in (V,Q) are locally isometric everywhere and hence form a single genus. We enumerate all orthogonal spaces (V,Q) of dimension at least 3, where the corresponding genus of maximal integral lattices consists of a single isometry class. It turns out, there are 471 such genera. Moreover, the dimension of V and the degree of K are bounded by 6 and 5 respectively. This classification also yields all maximal quaternion orders of type number one.}},
  author       = {{Kirschmer, Markus}},
  issn         = {{0022-314X}},
  journal      = {{Journal of Number Theory}},
  keywords     = {{Algebra and Number Theory}},
  pages        = {{375--393}},
  publisher    = {{Elsevier BV}},
  title        = {{{One-class genera of maximal integral quadratic forms}}},
  doi          = {{10.1016/j.jnt.2013.10.007}},
  volume       = {{136}},
  year         = {{2014}},
}

@article{34896,
  abstract     = {{We apply class field theory to the computation of the minimal discriminants for certain solvable groups. In particular, we apply our techniques to small Frobenius groups and all imprimitive degree 8 groups such that the corresponding fields have only a degree 2 and no degree 4 subfield.}},
  author       = {{Fieker, Claus and Klüners, Jürgen}},
  issn         = {{0022-314X}},
  journal      = {{Journal of Number Theory}},
  keywords     = {{Algebra and Number Theory}},
  number       = {{2}},
  pages        = {{318--337}},
  publisher    = {{Elsevier BV}},
  title        = {{{Minimal discriminants for fields with small Frobenius groups as Galois groups}}},
  doi          = {{10.1016/s0022-314x(02)00071-9}},
  volume       = {{99}},
  year         = {{2003}},
}