88 citations · 270 across the 33 of their papers we have counts for
5 papers · 2 filters
Statistics of Different Reduction Types of Fermat Curves
David Harvey, Igor Shparlinski
We present some theoretic bounds and algorithms concerning the statistics of different reduction types in the family of Fermat curves , where is prime and $s =1…
Counting points on hyperelliptic curves in average polynomial time
David Harvey
Let g >= 1 and let Q be a monic, squarefree polynomial of degree 2g + 1 in Z[x]. For an odd prime p not dividing the discriminant of Q, let Z_p(T) denote the zeta function of the h…
A search for Wilson primes
Edgar Costa, Robert Gerbicz, David Harvey
A Wilson prime is a prime p such that (p-1)! = -1 mod p^2. We report on a search for Wilson primes up to 2 * 10^13, and describe several new algorithms that were used in the search…
A subquadratic algorithm for computing the n-th Bernoulli number
David Harvey
We describe a new algorithm that computes the n-th Bernoulli number in n^(4/3 + o(1)) bit operations. This improves on previous algorithms that had complexity n^(2 + o(1)).
Faster deterministic integer factorization
Edgar Costa, David Harvey
The best known unconditional deterministic complexity bound for computing the prime factorization of an integer N is O(M_int(N^(1/4) log N)), where M_int(k) denotes the cost of mul…