Zobrazeno 1 - 10
of 375
pro vyhledávání: '"Lagarias, Jeffrey"'
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
An approximate divisor order is a partial order on the positive integers $\mathbb{N}^+$ that refines the divisor order and is refined by the additive total order. A previous paper studied such a partial order on $\mathbb{N}^+$, produced using the flo
Externí odkaz:
http://arxiv.org/abs/2403.04342
Autor:
Lagarias, Jeffrey C., Yangjit, Wijit
Publikováno v:
Journal of Number Theory 259 (2024) 131--170
This paper presents an extension of Bhargava's theory of factorials associated to any nonempty subset $S$ of $\mathbb{Z}$. Bhargava's factorials $k!_S$ are invariants, constructed using the notion of $p$-orderings of $S$ where $p$ is a prime. This pa
Externí odkaz:
http://arxiv.org/abs/2310.12949
Autor:
Lagarias, Jeffrey C., Sun, Chenyang
We consider two multiplicative statistics on the set of integer partitions: the norm of a partition, which is the product of its parts, and the supernorm of a partition, which is the product of the prime numbers $p_i$ indexed by its parts $i$. We int
Externí odkaz:
http://arxiv.org/abs/2308.15303
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
We improve upon the traditional error term in the truncated Perron formula for the logarithm of an $L$-function. All our constants are explicit.
Comment: 11 pages
Comment: 11 pages
Externí odkaz:
http://arxiv.org/abs/2206.01391
This paper studies an integer sequence $\overline{G}_n$ analogous to the product $G_n=\prod_{k=0}^n\binom{n}{k}$, the product of the elements of the $n$-th row of Pascal's triangle. It is known that $G_n=\prod_{p\le n}p^{\nu_p(G_n)}$ with $\nu_p(G_n)
Externí odkaz:
http://arxiv.org/abs/2112.14422
Autor:
Lagarias, Jeffrey C.
Publikováno v:
The Ultimate Challenge: The 3x+1 Problem, Edited by Jeffrey C. Lagarias. American Mathematical Society, Providence RI 2010, pp. 3--29
This paper is an overview and survey of work on the 3x+1 problem, also called the Collatz problem, and generalizations of it. It gives a history of the problem. It addresses two questions: (1) What can mathematics currently say about this problem? (a
Externí odkaz:
http://arxiv.org/abs/2111.02635
Autor:
Lagarias, Jeffrey C., Yangjit, Wijit
Publikováno v:
In Journal of Number Theory June 2024 259:131-170
