Zobrazeno 1 - 10
of 61
pro vyhledávání: '"11R29, 11R42"'
Publikováno v:
Research in number theory 9, 69, 2023
For a number field $K$, the Euler-Kronecker constant $\gamma_K$ associated to $K$ is an arithmetic invariant the size and nature of which is linked to some of the deepest questions in number theory. This theme was given impetus by Ihara who obtained
Externí odkaz:
http://arxiv.org/abs/2402.13127
In this paper we make explicit the constants of Habegger and Pazuki's work from 2017 on bounding the discriminant of cyclic Galois CM fields corresponding to genus 2 curves with CM by them and potentially good reduction outside a predefined set of pr
Externí odkaz:
http://arxiv.org/abs/2311.13403
We derive new cases of conjectures of Rubin and of Burns--Kurihara--Sano concerning derivatives of Dirichlet $L$-series at $s = 0$ in $p$-elementary extensions of number fields for arbitrary prime numbers $p$. In naturally arising examples of such ex
Externí odkaz:
http://arxiv.org/abs/2310.10468
Autor:
Tomé, Marie-Hélène
Deep work by Shintani in the 1970's describes Hecke $L$-functions associated to narrow ray class group characters of totally real fields $F$ in terms of what are now known as Shintani zeta functions. However, for $[F:\mathbb{Q}] = n \geq 3$, Shintani
Externí odkaz:
http://arxiv.org/abs/2307.16775
Autor:
McGown, Kevin J., Tucker, Amanda
We prove that the number of quartic fields $K$ with discriminant $|\Delta_K|\leq X$ whose Galois closure is $D_4$ equals $CX+O(X^{5/8+\varepsilon})$, improving the error term in a well-known result of Cohen, Diaz y Diaz, and Olivier. We prove an anal
Externí odkaz:
http://arxiv.org/abs/2307.14564
Autor:
Bordellès, Olivier
In this note, we provide an explicit upper bound for $h_K \mathcal{R}_K d_K^{-1/2}$ which depends on an effective constant in the error term of the Ideal Theorem.
Comment: 7 pages. Comments are welcome
Comment: 7 pages. Comments are welcome
Externí odkaz:
http://arxiv.org/abs/2207.11763
Autor:
Chirre, Andrés, Quesada-Herrera, Emily
We prove several results about integers represented by positive definite quadratic forms, using a Fourier analysis approach. In particular, for an integer $\ell\geq 1$, we improve the error term in the partial sums of the number of representations of
Externí odkaz:
http://arxiv.org/abs/2012.07781
Autor:
Mishra, Mohit
Let $d$ be a square-free positive integer and $h(d)$ the class number of the real quadratic field $\mathbb{Q}{(\sqrt{d})}.$ In this paper we give an explicit lower bound for $h(n^2+r)$, where $r=1,4$, and also establish an equivalent criteria to atta
Externí odkaz:
http://arxiv.org/abs/1906.09718
Groups of order $4$ are isomorphic to either $\mathbb{Z}/4\mathbb{Z}$ or $\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}$. We give certain sufficient conditions permitting to specify the structure of class groups of order $4$ in the family of r
Externí odkaz:
http://arxiv.org/abs/1902.05250
We obtain criteria for the class number of certain Richaud-Degert type real quadratic fields to be 3. We also treat a couple of families of real quadratic fields of Richaud-Degert type that were not considered earlier, and obtain similar criteria for
Externí odkaz:
http://arxiv.org/abs/1812.02488