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:1805.11066 (math)
[Submitted on 28 May 2018 (v1), last revised 9 Jul 2021 (this version, v3)]

Title:The density function for the value-distribution of the Lerch zeta-function and its applications

Authors:Masahiro Mine
View PDF
Abstract:The probabilistic study of the value-distributions of zeta-functions is one of the modern topics in analytic number theory. In this paper, we study a certain probability measure related to the value-distribution of the Lerch zeta-function. We prove that it has a density function which we can explicitly construct. Moreover, we prove an asymptotic formula for the number of zeros of the Lerch zeta-function on the right side of the critical line, whose main term is associated with the density function.
Comments: 37 pages
Subjects: Number Theory (math.NT)
MSC classes: 11M35
Cite as: arXiv:1805.11066 [math.NT]
  (or arXiv:1805.11066v3 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1805.11066
Journal reference: Michigan Math. J. 69 (2020) 849-889
Related DOI: https://doi.org/10.1307/mmj/1586570481

Submission history

From: Masahiro Mine [view email]
[v1] Mon, 28 May 2018 17:25:46 UTC (15 KB)
[v2] Wed, 12 Sep 2018 00:19:15 UTC (21 KB)
[v3] Fri, 9 Jul 2021 07:09:50 UTC (26 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?)