• Average Normalisations of Elliptic Curves 

    Banks, William David, 1964-; Shparlinski, Igor E. (Australian Mathematical Society, 2002)
    Ciet, Quisquater, and Sica have recently shown that every elliptic curve E over a finite field Fp is isomorphic to a curve y2 = x3 +ax+b with a and b of size O(p3/4). In this paper, we show that almost all elliptic curves ...
  • On the average value of divisor sums in arithmetic progressions 

    Banks, William David, 1964-; Heath-Brown, D. R.; Shparlinski, Igor E. (2005)
    We consider very short sums of the divisor function in arithmetic progressions prime to a fixed modulus and show that "on average" these sums are close to the expected value. We also give applications of our result to sums ...