Zobrazeno 1 - 10
of 42
pro vyhledávání: '"11R54"'
Autor:
Chan, Daniel, Lynch, Sean B.
In this manuscript, we give effective methods for computing the zeta function of maximal orders on surfaces.
Comment: 23 pages
Comment: 23 pages
Externí odkaz:
http://arxiv.org/abs/2410.16832
Autor:
Lynch, Sean B.
Lustig gave an infinite product formula for the zeta function of a commutative two-dimensional regular local ring with finite residue field. We extend this to the noncommutative setting with a method based on filtration by an invertible ideal. Our ma
Externí odkaz:
http://arxiv.org/abs/2310.15545
Autor:
Babei, Angelica, Herman, Allen
We calculate zeta functions for certain orders of rank $3$ defined by standard integral table algebras and integral fusion rings that have irrational-valued irreducible characters. The calculations are obtained from explicit calculations of zeta inte
Externí odkaz:
http://arxiv.org/abs/2304.13602
Autor:
Kopp, Gene S., Lagarias, Jeffrey C.
This paper contributes to the theory of orders of number fields. This paper defines a notion of "ray class group" associated to an arbitrary order in a number field together with an arbitrary ray class modulus for that order (including Archimedean da
Externí odkaz:
http://arxiv.org/abs/2212.09177
Autor:
Kirschmer, Markus, Klüners, Jürgen
We discuss various connections between ideal classes, divisors, Picard and Chow groups of one-dimensional noetherian domains. As a result of these, we give a method to compute Chow groups of orders in global fields and show that there are infinitely
Externí odkaz:
http://arxiv.org/abs/2208.14688
Autor:
O'Dorney, Evan M.
We prove a reflection theorem, conjectured by Nakagawa and Ohno, for the number of quartic rings, or pairs of ternary quadratic forms, with a given cubic resolvent. Over $\mathbb{Z}$, our results are unconditional; we also allow the base to be the ri
Externí odkaz:
http://arxiv.org/abs/2204.10924
Autor:
Babei, Angelica, Herman, Allen
We investigate Solomon's zeta function for orders in the special case of orders generated by the standard basis of an integral table algebra, a special case of which is the integral adjacency algebra of an association scheme. As Solomon's elementary
Externí odkaz:
http://arxiv.org/abs/2204.04784
Autor:
O'Dorney, Evan M.
The Ohno-Nakagawa (O-N) reflection theorem is an unexpectedly simple identity relating the number of $\mathrm{GL}_2 \mathbb{Z}$-classes of binary cubic forms (equivalently, cubic rings) of two different discriminants $D$, $-27D$; it generalizes cubic
Externí odkaz:
http://arxiv.org/abs/2111.09784
Autor:
O'Dorney, Evan M.
This is the original version of my Ph.D. thesis. The main results have been divided up between papers arXiv:2111.09784 and arXiv:2204.10924. This paper has been kept on the arXiv to preserve some proofs of elementary lemmas that will be removed from
Externí odkaz:
http://arxiv.org/abs/2107.04727
Autor:
Spelier, Pim
Given an order, a fundamental problem is deciding whether a univariate polynomial has a zero. It is a special case of deciding whether $\text{Hom}(A,B)$ is non-empty for two orders $A$ and $B$. For fixed separable orders, deciding whether a polynomia
Externí odkaz:
http://arxiv.org/abs/2101.06165