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:1812.11322 (math)
[Submitted on 29 Dec 2018 (v1), last revised 21 Mar 2019 (this version, v2)]

Title:On a $q$-deformation of modular forms

Authors:Victor J. W. Guo, Wadim Zudilin
View PDF
Abstract:There are many instances known when the Fourier coefficients of modular forms are congruent to partial sums of hypergeometric series. In our previous work arXiv:1803.01830, such partial sums are related to the radial asymptotics of infinite $q$-hypergeometric sums at roots of unity. Here we combine the two features to construct a hypergeometric $q$-deformation of two CM modular forms of weight 3 and discuss the corresponding $q$-congruences.
Comments: 13 pages
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG); Classical Analysis and ODEs (math.CA); Combinatorics (math.CO); Quantum Algebra (math.QA)
MSC classes: 11F33 (Primary), 11B65, 33C20, 33D15, 44A15
Cite as: arXiv:1812.11322 [math.NT]
  (or arXiv:1812.11322v2 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1812.11322
Journal reference: J. Math. Anal. Appl. 475:2 (2019), 1636--1646
Related DOI: https://doi.org/10.1016/j.jmaa.2019.03.035

Submission history

From: Wadim Zudilin [view email]
[v1] Sat, 29 Dec 2018 09:35:27 UTC (10 KB)
[v2] Thu, 21 Mar 2019 13:34:24 UTC (10 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.NT
< prev   |   next >
new | recent | 2018-12
Change to browse by:
math
math.AG
math.CA
math.CO
math.QA

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?)