Roy Shmueli

I am a Ph.D. in mathematics, working at Jether Energy, where I focus on data analysis and research of energy markets in USA and Europe.

During my studies in Tel Aviv University, I worked on the random polynomials over finite and local fields.

Selected Publications

Preprint

Irreducibility of Polynomials with Square Coefficients over Finite Fields

Bary-Soroker, Lior, and Shmueli, Roy

arXiv preprint arXiv:2410.16814 , October 2024

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We study a random polynomial of degree n over the finite field \mathbbF_q, where the coefficients are independent and identically distributed and uniformly chosen from the squares in \mathbbF_q. Our main result demonstrates that the likelihood of such a polynomial being irreducible approaches 1/n + O(q^-1/2) as the field size q grows infinitely large. The analysis we employ also applies to polynomials with coefficients selected from other specific sets.
Preprint

The number of roots of a random polynomial over the field of p-adic numbers

Shmueli, Roy

arXiv preprint arXiv:2204.03473 , April 2022

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We study the roots of a random polynomial over the field of p-adic numbers. For a random monic polynomial with coefficients in Z_p, we obtain an asymptotic formula for the factorial moments of the number of roots of this polynomial. In addition, we show the probability that a random polynomial of degree n has more than log(n) roots is O(n-K) for some K>0.
Journal

The expected number of roots over the field of p-adic numbers

Shmueli, Roy

International Mathematics Research Notices , November 2021

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We study the roots of a random polynomial over the field of p-adic numbers. For a random monic polynomial with i.i.d. coefficients in Zp, we obtain an estimate for the expected number of roots of this polynomial. In particular, if the coefficients take the values ±1 with equal probability, the expected number of p-adic roots converges to (p-1)/(p+1) as the degree of the polynomial tends to ∞.