Using a probabilistic method for number theoretic purposes, I have encountered the following question (it may be very standard):



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> Let $X\_t$ be a Gaussian process $(t>0)$ such that $X\_0=0$. What is the expected number of times for the process to cross zero in the interval $[0,c)$ as a function of $c$?
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Number of times a Gaussian process crosses zero in an interval
The magic words are "Kac-Rice formula". This is exactly the question which comes up in analyzing zeros of random polynomials.


