• Irrationality of Power Series for Various Number Theoretic Functions 

    Banks, William David, 1964-; Luca, Florian; Shparlinski, Igor E. (2005-10)
    We study formal power series whose coefficients are taken to be a variety of number theoretic functions, such as the Euler, Möbius and divisor functions. We show that these power series are irrational over ℤ [X], and we ...
  • Short Kloosterman Sums for Polynomials over Finite Fields 

    Banks, William David, 1964-; Harcharras, Asma; Shparlinski, Igor E. (2003)
    We extend to the setting of polynomials over a finite field certain estimates for short Kloosterman sums originally due to Karatsuba. Our estimates are then used to establish some uniformity of distribution results in the ...