# Tag Info

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• 5,606
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### Approximation for a series involving the derivative of a Jacobi theta function

Write your $\Lambda$ as $$\Lambda(t)=\frac{1}{2}\sum_{-\infty}^\infty f(n),$$ where $$f(x)=\pi(x+1/2)\sin\pi(x+1/2)\exp\left(-\pi^2(x+1/2)^2t/2\right)=y\sin y\,e^{-ty^2/2},$$ where $y=\pi(x+1/2),$ and ...
• 90.1k

### Siegel modular forms in Mathematica

You might want to check out the documentation on Siegel Modular Forms by Yuen, Poor, Shurman, and King. It provides a variety of Mathematica and Maple notebooks.
• 183k
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• 2,624
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### 2D lattice sum with numerator

The $n=4$ sum is accessible as follows. Expand $(j+k)^4$; by symmetry the odd terms $4j^3k$ and $4jk^3$ cancel out so we need only sum $(j^4 + 6j^2k^2 + k^4) / (j^2+k^2)^4$. You say you already know ...
• 78.4k
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• 2,738
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### Lower bound for the number of representations of integers as sum of squares

For $k=4$, your statement would be that $r_4(n) \gg n^{1-\epsilon}$. This is false. Jacobi's four-square theorem can be stated as that $r_4(n)/8$ is the sum of the divisors of $n$ that are not ...
• 27.9k
### Infinite product of $1-q^{n^2}$
Write $\theta(q)=\sum_{n \in \mathbb Z} q^{n^2}$. Taking logarithms, we get that the logarithm of your function is \$\sum_n \ln(1-q^{n^2}) = -\sum_n \sum_m \frac 1 m q^{n^2m} = -\sum_m \frac 1 m \frac {...