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:1408.3394 (math)
[Submitted on 14 Aug 2014 (v1), last revised 3 Sep 2014 (this version, v3)]

Title:Mean-Value of Product of Shifted Multiplicative Functions and Average Number of Points on Elliptic Curves

Authors:R. Balasubramanian, Sumit Giri
View PDF
Abstract:In this paper, we consider the mean value of the product of two real valued multiplicative functions with shifted arguments. The functions $F$ and $G$ under consideration are close to two nicely behaved functions $A$ and $B$, such that the average value of $A(n-h)B(n)$ over any arithmetic progression is only dependent on the common difference of the progression. We use this method on the problem of finding mean value of $K(N)$, where $K(N)/\log N$ is the expected number of primes such that a random elliptic curve over rationals has $N$ points when reduced over those primes.
Comments: In this version the overall presentation has been changed by keeping the main result fixed
Subjects: Number Theory (math.NT)
Cite as: arXiv:1408.3394 [math.NT]
  (or arXiv:1408.3394v3 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1408.3394

Submission history

From: Sumit Giri [view email]
[v1] Thu, 14 Aug 2014 19:20:10 UTC (9 KB)
[v2] Fri, 15 Aug 2014 05:26:50 UTC (1 KB) (withdrawn)
[v3] Wed, 3 Sep 2014 19:53:03 UTC (10 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.NT
< prev   |   next >
new | recent | 2014-08
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?)