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- ItemRational conjugacy classes of maximal tori in groups of Dn(World Scientific, 2021) Fiori, AndrewWe give a concrete characterization of the rational conjugacy classes of maximal tori in groups of type Dn, with specific emphasis on the case of number fields and p-adic fields. This includes the forms associated to quadratic spaces, all of their inner and outer forms as well as the Spin groups, their simply connected covers. In particular, in this work, we handle all (simply connected) outer forms of D4.
- ItemStrengthening the Baillie-PSW primality test(American Mathematical Society, 2021) Baillie, Robert; Fiori, Andrew; Wagstaff, Samuel S.In 1980, the first and third authors proposed a probabilistic primality test that has become known as the Baillie-PSW primality test. Its power to distinguish between primes and composites comes from combining a Fermat probable prime test with a Lucas probable prime test. No odd composite integers have been reported to pass this combination of primality tests if the parameters are chosen in an appropriate way. Here, we describe a significant strengthening of this test that comes at almost no additional computational cost. This is achieved by including in the test Lucas-V pseudoprimes, of which there are only five less than 10 (15)
- ItemAverage liar count for degree-2 Frobenius pseudoprimes(American Mathematical Society, 2020) Fiori, Andrew; Shallue, AndrewIn this paper we obtain lower and upper bounds on the average number of liars for the Quadratic Frobenius Pseudoprime Test of Grantham [Math. Comp. 70 (2001), pp. 873–891], generalizing arguments of Erdős and Pomerance [Math. Comp. 46 (1986), pp. 259–279] and Monier [Theoret. Comput. Sci. 12 (1980), 97–108]. These bounds are provided for both Jacobi symbol cases, providing evidence for the existence of several challenge pseudoprimes.