Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Number Theory

arXiv:1804.08483 (math)
[Submitted on 23 Apr 2018 (v1), last revised 6 May 2018 (this version, v2)]

Title:Erdős' Multiplication Table Problem for Function Fields and Symmetric Groups

Authors:Patrick Meisner
View PDF
Abstract:Erdős first showed that the number of positive integers up to $x$ which can be written as a product of two number less than $\sqrt{x}$ has zero density. Ford then found the correct order of growth of the set of all these integers. We will use the tools developed by Ford to answer the analogous question in the function field setting. Finally, we will use a classical result relating factorization of polynomials to factorization of permutations to recover a result of Eberhard, Ford and Green of an analogous multiplication table problem for permutations.
Subjects: Number Theory (math.NT)
Cite as: arXiv:1804.08483 [math.NT]
  (or arXiv:1804.08483v2 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1804.08483

Submission history

From: Patrick Meisner [view email]
[v1] Mon, 23 Apr 2018 14:57:27 UTC (12 KB)
[v2] Sun, 6 May 2018 08:11:07 UTC (15 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.NT
< prev   |   next >
new | recent | 2018-04
Change to browse by:
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)