All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 7 Next

Displaying 121 – 140 of 141

Showing per page

Two identities related to Dirichlet character of polynomials

Weili Yao, Wenpeng Zhang (2013)

Czechoslovak Mathematical Journal

Let q be a positive integer, χ denote any Dirichlet character mod q . For any integer m with ( m , q ) = 1 , we define a sum C ( χ , k , m ; q ) analogous to high-dimensional Kloosterman sums as follows: C ( χ , k , m ; q ) = ∑ a 1 = 1 q ' ∑ a 2 = 1 q ' ⋯ ∑ a k = 1 q ' χ ( a 1 + a 2 + ⋯ + a k + m a 1 a 2 ⋯ a k ¯ ) , where a · a ¯ ≡ 1 mod q . The main purpose of this paper is to use elementary methods and properties of Gauss sums to study the computational problem of the absolute value | C ( χ , k , m ; q ) | , and give two interesting identities for it.

Upper bounds for certain trigonometric sums involving cosine powers

Anastasios D. Simalarides (2015)

Colloquium Mathematicae

We establish upper bounds for certain trigonometric sums involving cosine powers. Part of these results extend previous ones valid for the sum ∑ m = 1 k - 1 | s i n ( π r m / k ) | / s i n ( π m / k ) . We apply our results to estimate character sums in an explicit and elementary way.

Visible Points on Curves over Finite Fields

Igor E. Shparlinski, José Felipe Voloch (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

For a prime p and an absolutely irreducible modulo p polynomial f(U,V) ∈ ℤ[U,V] we obtain an asymptotic formula for the number of solutions to the congruence f(x,y) ≡ a (mod p) in positive integers x ≤ X, y ≤ Y, with the additional condition gcd(x,y) = 1. Such solutions have a natural interpretation as solutions which are visible from the origin. These formulas are derived on average over a for a fixed prime p, and also on average over p for a fixed integer a.

Currently displaying 121 – 140 of 141