Zobrazeno 1 - 10
of 699
pro vyhledávání: '"11r37"'
Autor:
Kopp, Gene S.
We give a new interpretation of Stark units associated to real quadratic fields as real multiplication values of a modular cocycle. The cocycle of interest is a meromorphic factor describing the modular transformations of the $q$-Pochhammer symbol an
Externí odkaz:
http://arxiv.org/abs/2411.06763
Autor:
Liu, Qi, Xing, Zugan
For a prime p, we study the Galois groups of maximal pro-$p$ extensions of imaginary quadratic fields unramified outside a finite set $S$, where $S$ consists of one or two finite places not lying above $p$. When $p$ is odd, we give explicit presentat
Externí odkaz:
http://arxiv.org/abs/2411.03155
Autor:
Gundlach, Fabian
Let $G$ be a finite abelian $p$-group. We count $G$-extensions of global rational function fields $\mathbb F_q(T)$ of characteristic $p$ by the degree of what we call their Artin-Schreier conductor. The corresponding (ordinary) generating function tu
Externí odkaz:
http://arxiv.org/abs/2410.23964
Autor:
Potthast, Nicolas
We determine the distribution of discriminants of wildly ramified elementary-abelian extensions of local and global function fields in characteristic $p$. For local and rational function fields, we also give precise formulae for the number of element
Externí odkaz:
http://arxiv.org/abs/2408.16394
Autor:
Maarefparvar, Abbas
We prove two conjectures proposed by Chabert and Halberstadt concerning P\'olya groups of $S_4$-fields and $D_4$-fields. More generally, the latter will be proved for $D_n$-fields with $n \geq 4$ an even integer. Further, generalizing a result of Zan
Externí odkaz:
http://arxiv.org/abs/2408.09019
Autor:
Mishra, Bhawesh
Let $n$ be a natural number greater than $2$ and $q$ be the smallest prime dividing $n$. We show that a finite subset $A$ of rationals, of cardinality at most $q$, contains a $n^{th}$ power in $\mathbb{Q}_{p}$ for almost every prime $p$ if and only i
Externí odkaz:
http://arxiv.org/abs/2408.03301
Autor:
Tavernier, Julie
We study the distribution of abelian number fields with frobenian conditions imposed on the conductor. In particular we find an asymptotic for the number of abelian field extensions of a number field k whose conductor is the sum of two squares. We al
Externí odkaz:
http://arxiv.org/abs/2407.14341
Autor:
Kopp, Gene S., Lagarias, Jeffrey C.
We consider the problem of counting and classifying symmetric informationally complete positive operator-valued measures (SICs or SIC-POVMs), that is, sets of $d^2$ equiangular lines in $\mathbb{C}^d$. For $4 \leq d \leq 90$, we show the number of kn
Externí odkaz:
http://arxiv.org/abs/2407.08048
Autor:
McConnell, Gary
Fix a finite collection of primes $\{ p_j \}$, not containing $2$ or $3$. Using some observations which arose from attempts to solve the SIC-POVMs problem in quantum information, we give a simple methodology for constructing an infinite family of sim
Externí odkaz:
http://arxiv.org/abs/2406.14632
Astonishing new discoveries with quartets and octets of cyclic cubic fields sharing a common conductor are presented. Four kinds of graphs describing cubic residue conditions among the prime divisors of the conductor enforce elementary bi- or tricycl
Externí odkaz:
http://arxiv.org/abs/2406.06030