@article{55276,
  author       = {{Minelli, P. and Sourmelidis, A. and Technau, Marc}},
  journal      = {{Int. Math. Res. Not. IMRN}},
  number       = {{10}},
  pages        = {{8485–8502}},
  title        = {{{On restricted averages of Dedekind sums}}},
  doi          = {{10.1093/imrn/rnad283}},
  volume       = {{2024}},
  year         = {{2024}},
}

@article{55278,
  author       = {{Technau, Marc}},
  journal      = {{Proc. Amer. Math. Soc.}},
  number       = {{1}},
  pages        = {{63–69}},
  title        = {{{Remark on the Farey fraction spin chain}}},
  doi          = {{10.1090/proc/16520}},
  volume       = {{152}},
  year         = {{2024}},
}

@article{49372,
  author       = {{Klüners, Jürgen and Wang, Jiuya}},
  issn         = {{2730-9657}},
  journal      = {{La Matematica}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Idélic Approach in Enumerating Heisenberg Extensions}}},
  doi          = {{10.1007/s44007-023-00067-w}},
  year         = {{2023}},
}

@article{55277,
  author       = {{Klahn, B. and Technau, Marc}},
  journal      = {{Int. J. Number Theory}},
  number       = {{10}},
  pages        = {{2443–2450}},
  title        = {{{Galois groups of (ⁿ₀)+(ⁿ₁)X+…+(ⁿ₆)X⁶}}},
  doi          = {{10.1142/S1793042123501208}},
  volume       = {{19}},
  year         = {{2023}},
}

@article{55279,
  author       = {{Minelli, P. and Sourmelidis, A. and Technau, Marc}},
  journal      = {{Math. Ann.}},
  pages        = {{291–320}},
  title        = {{{Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums}}},
  doi          = {{10.1007/s00208-022-02452-2}},
  volume       = {{387}},
  year         = {{2023}},
}

@article{55280,
  author       = {{Elsholtz, Ch. and Klahn, B. and Technau, Marc}},
  journal      = {{Acta Arith.}},
  number       = {{3}},
  pages        = {{251–263}},
  title        = {{{On polynomials with roots modulo almost all primes}}},
  doi          = {{10.4064/aa220407-9-7}},
  volume       = {{205:3}},
  year         = {{2022}},
}

@article{34839,
  abstract     = {{We describe the relations among the ℓ-torsion conjecture, a conjecture of Malle giving an upper bound for the number of extensions, and the discriminant multiplicity conjecture. We prove that the latter two conjectures are equivalent in some sense. Altogether, the three conjectures are equivalent for the class of solvable groups. We then prove the ℓ-torsion conjecture for ℓ-groups and the other two conjectures for nilpotent groups.}},
  author       = {{Klüners, Jürgen and Wang, Jiuya}},
  issn         = {{0002-9939}},
  journal      = {{Proceedings of the American Mathematical Society}},
  keywords     = {{Applied Mathematics, General Mathematics}},
  number       = {{7}},
  pages        = {{2793--2805}},
  publisher    = {{American Mathematical Society (AMS)}},
  title        = {{{ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group}}},
  doi          = {{10.1090/proc/15882}},
  volume       = {{150}},
  year         = {{2022}},
}

@article{34835,
  abstract     = {{We prove an upper bound for the asymptotics of counting functions of number fields with nilpotent Galois groups. }},
  author       = {{Klüners, Jürgen}},
  issn         = {{0065-1036}},
  journal      = {{Acta Arithmetica}},
  keywords     = {{Algebra and Number Theory}},
  number       = {{2}},
  pages        = {{165--184}},
  publisher    = {{Institute of Mathematics, Polish Academy of Sciences}},
  title        = {{{The asymptotics of nilpotent Galois groups}}},
  doi          = {{10.4064/aa211207-16-5}},
  volume       = {{204}},
  year         = {{2022}},
}

@article{45854,
  abstract     = {{In a previous paper the authors developed an algorithm to classify certain quaternary quadratic lattices over totally real fields. The present article applies this algorithm to the classification of binary Hermitian lattices over totally imaginary fields. We use it in particular to classify the 48-dimensional extremal even unimodular lattices over the integers that admit a semilarge automorphism.}},
  author       = {{Kirschmer, Markus and Nebe, Gabriele}},
  issn         = {{1058-6458}},
  journal      = {{Experimental Mathematics}},
  keywords     = {{General Mathematics}},
  number       = {{1}},
  pages        = {{280--301}},
  publisher    = {{Informa UK Limited}},
  title        = {{{Binary Hermitian Lattices over Number Fields}}},
  doi          = {{10.1080/10586458.2019.1618756}},
  volume       = {{31}},
  year         = {{2022}},
}

@article{55290,
  author       = {{Baier, St. and Mazumder, D. and Technau, Marc}},
  journal      = {{Unif. Distrib. Theory}},
  number       = {{2}},
  pages        = {{1–48}},
  title        = {{{On the distribution of αp modulo one in quadratic number fields}}},
  doi          = {{10.2478/udt-2021-0006}},
  volume       = {{16}},
  year         = {{2021}},
}

@article{55289,
  author       = {{Technau, Marc and Zafeiropoulos, A.}},
  journal      = {{Acta Arith.}},
  number       = {{1}},
  pages        = {{93–104}},
  title        = {{{Metric results on summatory arithmetic functions on Beatty sets}}},
  doi          = {{10.4064/aa200128-10-6}},
  volume       = {{197}},
  year         = {{2021}},
}

@article{34840,
  abstract     = {{In this paper we obtain a complete list of imaginary n-quadratic fields with class groups of exponent 3 and 5 under ERH for every positive integer n where an n-quadratic field is a number field of degree 2ⁿ represented as the composite of n quadratic fields. }},
  author       = {{Klüners, Jürgen and Komatsu, Toru}},
  issn         = {{0025-5718}},
  journal      = {{Mathematics of Computation}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Algebra and Number Theory}},
  number       = {{329}},
  pages        = {{1483--1497}},
  publisher    = {{American Mathematical Society (AMS)}},
  title        = {{{Imaginary multiquadratic number fields with class group of exponent $3$ and $5$}}},
  doi          = {{10.1090/mcom/3609}},
  volume       = {{90}},
  year         = {{2021}},
}

@article{34912,
  abstract     = {{Let E be an ordinary elliptic curve over a finite field and g be a positive integer. Under some technical assumptions, we give an algorithm to span the isomorphism classes of principally polarized abelian varieties in the isogeny class of E⁹ . The varieties are first described as hermitian lattices over (not necessarily maximal) quadratic orders and then geometrically in terms of their algebraic theta null point. We also show how to algebraically compute Siegel modular forms of even weight given as polynomials in the theta constants by a careful choice of an affine lift of the theta null point. We then use these results to give an algebraic computation of Serre’s obstruction for principally polarized abelian threefolds isogenous to E³ and of the Igusa modular form in dimension 4. We illustrate our algorithms with examples of curves with many rational points over finite fields. }},
  author       = {{Kirschmer, Markus and Narbonne, Fabien and Ritzenthaler, Christophe and Robert, Damien}},
  issn         = {{0025-5718}},
  journal      = {{Mathematics of Computation}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Algebra and Number Theory}},
  number       = {{333}},
  pages        = {{401--449}},
  publisher    = {{American Mathematical Society (AMS)}},
  title        = {{{Spanning the isogeny class of a power of an elliptic curve}}},
  doi          = {{10.1090/mcom/3672}},
  volume       = {{91}},
  year         = {{2021}},
}

@article{55288,
  author       = {{Baier, St. and Technau, Marc}},
  journal      = {{J. Théor. Nombres Bordx.}},
  number       = {{2}},
  pages        = {{719–760}},
  title        = {{{On the distribution of αp modulo one in imaginary quadratic number fields with class number one}}},
  doi          = {{10.5802/jtnb.1141}},
  volume       = {{32}},
  year         = {{2020}},
}

@article{55286,
  author       = {{Technau, Marc}},
  journal      = {{J. Number Theory}},
  pages        = {{148–167}},
  title        = {{{Modular hyperbolas and Beatty sequences}}},
  doi          = {{10.1016/j.jnt.2019.07.022}},
  volume       = {{208}},
  year         = {{2020}},
}

@article{55287,
  author       = {{Shparlinski, I. E. and Technau, Marc}},
  journal      = {{Funct. Approximatio, Comment. Math.}},
  number       = {{1}},
  pages        = {{113–124}},
  title        = {{{Kloosterman sums with twice-differentiable functions}}},
  doi          = {{10.7169/facm/1845}},
  volume       = {{63}},
  year         = {{2020}},
}

@article{55283,
  author       = {{Barth, D. and Beck, M. and Dose, T. and Glaßer, Ch. and Michler, L. and Technau, Marc}},
  journal      = {{Theoretical Computer Science}},
  pages        = {{11–35}},
  title        = {{{Emptiness problems for integer circuits}}},
  doi          = {{10.1016/j.tcs.2020.03.023}},
  volume       = {{824-825}},
  year         = {{2020}},
}

@article{34842,
  abstract     = {{Let D<0 be a fundamental discriminant and denote by E(D) the exponent of the ideal class group Cl(D) of K=ℚ(√D). Under the assumption that no Siegel zeros exist we compute all such D with E(D) dividing 8. We compute all D with |D| ≤ 3.1⋅10²⁰ such that E(D) ≤ 8.}},
  author       = {{Elsenhans, Andreas-Stephan and Klüners, Jürgen and Nicolae, Florin}},
  issn         = {{0065-1036}},
  journal      = {{Acta Arithmetica}},
  keywords     = {{Algebra and Number Theory}},
  number       = {{3}},
  pages        = {{217--233}},
  publisher    = {{Institute of Mathematics, Polish Academy of Sciences}},
  title        = {{{Imaginary quadratic number fields with class groups of small exponent}}},
  doi          = {{10.4064/aa180220-20-3}},
  volume       = {{193}},
  year         = {{2020}},
}

@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{34917,
  abstract     = {{We relate proper isometry classes of maximal lattices in a totally definite quaternary quadratic space (V,q) with trivial discriminant to certain equivalence classes of ideals in the quaternion algebra representing the Clifford invariant of (V,q). This yields a good algorithm to enumerate a system of representatives of proper isometry classes of lattices in genera of maximal lattices in (V,q).}},
  author       = {{Kirschmer, Markus and Nebe, Gabriele}},
  issn         = {{1793-0421}},
  journal      = {{International Journal of Number Theory}},
  keywords     = {{Algebra and Number Theory}},
  number       = {{02}},
  pages        = {{309--325}},
  publisher    = {{World Scientific Pub Co Pte Lt}},
  title        = {{{Quaternary quadratic lattices over number fields}}},
  doi          = {{10.1142/s1793042119500131}},
  volume       = {{15}},
  year         = {{2019}},
}