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:1805.09008 (math)
[Submitted on 23 May 2018 (v1), last revised 28 Aug 2019 (this version, v3)]

Title:On the average number of representations of an integer as a sum of like prime powers

Authors:Marco Cantarini, Alessandro Gambini, Alessandro Zaccagnini
View PDF
Abstract:We investigate the average number of representations of a positive integer as the sum of $k + 1$ perfect $k$-th powers of primes. We extend recent results of Languasco and the last Author, which dealt with the case $k = 2$ [6] and $k = 3$ [5] respectively. We use the same technique to study the corresponding problem for sums of just $k$ perfect $k$-th powers of primes.
Comments: Final version. References updated. To appear in Proc. AMS
Subjects: Number Theory (math.NT)
Cite as: arXiv:1805.09008 [math.NT]
  (or arXiv:1805.09008v3 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1805.09008
Journal reference: Proc. Amer. Math. Soc. 148.4 (2020), 1499-1508
Related DOI: https://doi.org/10.1090/proc/14827

Submission history

From: Alessandro Zaccagnini [view email]
[v1] Wed, 23 May 2018 08:20:31 UTC (8 KB)
[v2] Tue, 5 Jun 2018 16:42:23 UTC (9 KB)
[v3] Wed, 28 Aug 2019 07:14:08 UTC (9 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.NT
< prev   |   next >
new | recent | 2018-05
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?)