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Results tagged with modular-forms
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user 10475
Questions about modular forms and related areas
19
votes
Accepted
Are umbral moonshine and umbral calculus connected?
We used the word "umbral" because umbral moonshine involves mock modular forms whose lack of modularity is characterized by another function known as the shadow of the mock modular form. Umbra is the …
- 5,546
2
votes
What is the relationship between the Leech lattice and Dedekind eta function?
Steve Carnahan in his answer to this question Where do the product expansions of modular forms come from?
gives a conceptual explanation of the product form for $\Delta$, but it has nothing to do with …
- 5,546
4
votes
Accepted
Index one weak Jacobi forms and weakly holomorphic modular forms?
Section 4.2 of this paper https://arxiv.org/pdf/1208.4074.pdf
by Dabholkar, Murthy and Zagier may be what you want. The theta coefficients of weak Jacobi forms of weight k and index m are 2m component …
- 5,546
8
votes
2
answers
805
views
Reference request for Hecke operators for principal congruence subgroup of modular group
I am looking for references that discuss Hecke operators $T_n$ acting on modular forms
for the principal congruence subgroup $\Gamma(N)$ of the modular group $SL(2,Z)$ and am happy to restrict to the …
- 5,546
6
votes
0
answers
430
views
More on Moonshine for the Thompson group and weakly holomorphic weight one half modular forms
This question is a follow-up to
Monstrous Moonshine for Thompson group $Th$?
and is based on various comments to that question, in particular S. Carnahan's mention of the
connection to known Moonshin …
- 5,546
11
votes
Accepted
Monstrous moonshine for $M_{24}$ and K3?
I can answer your first question. In arXiv:1208.4074 by Dabholkar, Murthy and Zagier you can find a formula that implies
$H^{(2)}(\tau)= \frac{48 F_2^{(2)}(\tau)- 2 E_2(\tau)}{\eta(\tau)^3}$
where $E_ …
- 5,546
12
votes
Accepted
Computing Thompson series for the monster group
From MathSciNet:
MR1037906 (90m:11065) Reviewed
McKay, John(3-CONC); Strauss, Hubertus(3-CONC)
The q-series of monstrous moonshine and the decomposition of the head characters.
Comm. Algebra 18 (19 …
- 5,546
8
votes
Accepted
Mock Theta Functions
In addition to Zagier's excellent Bourbaki seminar I would also recommend some notes by Ken Ono that include both a summary of the history of mock theta functions and mock modular forms and a survey o …
- 5,546
6
votes
2
answers
1k
views
What is the modern understanding of the order of a mock theta function?
Ramanujan introduced mock theta functions and described them by an "order" which he did not define. As a result of the work of Zwegers and others we now have a better understanding of mock theta funct …
- 5,546