# Questions tagged [roots]

Questions about the set of values at which a given function evaluates to zero. For questions about "square roots", "cube roots" and such, consider using the (radicals) and the (arithmetic) tag. For questions about roots of Lie algebras, use the (lie-algebra) tag instead.

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### A root finding problem

While solving a partial differential equation, I obtained the following function: $$F(z)=(k^2 - z^2)J_1^2(z)-z^2J_0^2(z) \tag 1$$ where $k \in (1, \sqrt2)$ and $z$ is a complex variable. I need to ...
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### "Are there any simple groups that appear as zeros of the zeta function?" by Peter Freyd; why is this consternating to mathematicians?

I would like to understand the "upsetting"-to-mathematicians nature of this question Freyd poses to demonstrate that "any language sufficiently rich that to be defined necessarily ...
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### Asymptotic roots of equation involving Bessel functions

Let $r_2>r_1>0$, $g\ge 0$, and let $\lambda_n$, $n=1,2,\ldots,\infty$, be the positive roots of $$J_g(xr_2)Y_g'(xr_1)-J_g'(xr_1)Y_g(xr_2)=0,$$ where $J_g'(xr_1)$ is ...
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### Natural roots of multivariate integer polynomials

I know the problem of determining whether a multivariate integer polynomial has integer roots is in general undecidable. However, does this change when we consider only its natural roots?
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