THE PROGRAM ayb: This is a program for checking both Conjecture 6.1 (upper bound conjecture, also known as the sharp conjecture) and Conjecture 6.2 (covering conjecture) for Weil sums of binomials. The usage is ayb [c/s] smallest_modulus_plus_one largest_modulus_plus_one The [c/s] is either "s" for checking the sharp conjecture (Conjecture 6.1) or "c" for checking the covering conjecture (Conjecture 6.2). smallest_modulus_plus_one and largest_modulus_plus_one: With option "s" the program will check Conjecture 6.1 for all finite fields whose orders are between these two sizes (inclusive of an endpoint if it is a prime power). With option "c" the program will check Conjecture 6.2 for all moduli t^n-1 such that t^n is between these two sizes (inclusive of endpoints, if feasible). The smallest_modulus_plus_one must be at least 32 (smaller values are verified trivially by Theorem 1.1 for the Conjecture 6.1 or by Lemma 6.8 for Conjecture 6.2) and the largest_modulus_plus_one must of course be at least the smallest_modulus_plus_one. results are printed to standard output ============================================================ THE DATA, ORGANIZED BY CONJECTURE Conjecture 6.1. The verification is documented in sharp-ten-to-thirteen.txt whose contents are all described in sharp-ten-to-thirteen-summary.txt and these files are produced as outputs by running ./ayb s 32 10000000000000 ------------------------------------------------------------ Conjecture 6.2. The verification is documented in covering-three-times-ten-to-nine.txt whose contents are all described in covering-three-times-ten-to-nine-summary.txt and these files are produced as outputs by running ./ayb c 32 3000000000