2023/08/28 by Ritik Jain, Jain, Ritik, Han‐Bom Moon +3
Mathematics · #Mathematical Dynamics and Fractals #Mathematical functions and polynomials #Analytic Number Theory Research
paper · pdf · doi:10.48550/arxiv.2308.14580
We study the probability distribution of the number of zeros of multivariable polynomials with bounded degree over a finite field. We find the probability generating function for each set of bounded degree polynomials. In particular, in the single variable case, we show that as the degree of the polynomials and the order of the field simultaneously approach infinity, the distribution converges to a Poisson distribution.