On Fully Split Lacunary Polynomials in Finite Fields

Volume 59 / 2011

Khodakhast Bibak, Igor E. Shparlinski Bulletin Polish Acad. Sci. Math. 59 (2011), 197-202 MSC: Primary 11T06; Secondary 05C69. DOI: 10.4064/ba59-3-1


We estimate the number of possible degree patterns of $k$-lacunary polynomials of degree $t < p$ which split completely modulo $p$. The result is based on a combination of a bound on the number of zeros of lacunary polynomials with some graph theory arguments.


  • Khodakhast BibakDepartment of Combinatorics and Optimization
    University of Waterloo
    Waterloo, Ontario, Canada N2L 3G1
  • Igor E. ShparlinskiDepartment of Computing
    Macquarie University
    Sydney, NSW 2109, Australia

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