- #1
jostpuur
- 2,112
- 19
Assuming that I understood correctly one claim from the Riemann's On the Number of Prime Numbers less than a Given Quantity, then if we define a function
<br /> \psi:]0,\infty[\to\mathbb{R},\quad \psi(x) = \sum_{n=1}^{\infty} e^{-n^2\pi x},<br />
it satisfies an equation
<br /> 2\psi(x) + 1 = x^{-\frac{1}{2}}\Big(2\psi\big(\frac{1}{x}\big) + 1\Big).<br />
Anyone knowing how to prove that?
<br /> \psi:]0,\infty[\to\mathbb{R},\quad \psi(x) = \sum_{n=1}^{\infty} e^{-n^2\pi x},<br />
it satisfies an equation
<br /> 2\psi(x) + 1 = x^{-\frac{1}{2}}\Big(2\psi\big(\frac{1}{x}\big) + 1\Big).<br />
Anyone knowing how to prove that?
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