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Distribution of values of Hecke characters of infinite order

C. S. Rajan (1998)

Acta Arithmetica

We show that the number of primes of a number field K of norm at most x, at which the local component of an idele class character of infinite order is principal, is bounded by O(x exp(-c√(log x))) as x → ∞, for some absolute constant c > 0 depending only on K.

Distributional properties of powers of matrices

Fernando Chamizo, Dulcinea Raboso (2014)

Czechoslovak Mathematical Journal

We apply the larger sieve to bound the number of 2 × 2 matrices not having large order when reduced modulo the primes in an interval. Our motivation is the relation with linear recursive congruential generators. Basically our results establish that the probability of finding a matrix with large order modulo many primes drops drastically when a certain threshold involving the number of primes and the order is exceeded. We also study, for a given prime and a matrix, the existence of nearby non-similar...

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