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Results tagged with nt.number-theory
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user 10475
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
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
Number theory and physics
The rational numbers $\mathbb{Q}$ are central to number theory, so I think it would be reasonable to claim a connection between number theory and ``real” physics if there were a physical system with p …
- 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