• Character Sums over Integers with Restricted g-ary Digits 

    Banks, William David, 1964-; Conflitti, Alessandro; Shparlinski, Igor E. (2002)
    We establish upper bounds for multiplicative character sums and exponential sums over sets of integers that are described by various properties of their digits in a fixed base g ≥ 2. Our main tools are the Weil and ...
  • Exponential Sums over Mersenne Numbers 

    Banks, William David, 1964-; Conflitti, Alessandro; Friedlander, J. B. (John B.); Shparlinski, Igor E. (2004)
    We give estimates for exponential sums of the form Σn≤N Λ(n) exp(2πiagn/m), where m is a positive integer, a and g are integers relatively prime to m, and Λ is the von Mangoldt function. In particular, our results yield ...
  • Number Theoretic Designs for Directed Regular Graphs of Small Diameter 

    Banks, William David, 1964-; Conflitti, Alessandro; Shparlinski, Igor E. (Society for Industrial and Applied Mathematics, 2004)
    In 1989, F. R. K. Chung gave a construction for certain directed h-regular graphs of small diameter. Her construction is based on finite fields, and the upper bound on the diameter of these graphs is derived from bounds ...