9 Result(s)

Article

Distribution of Primitive λ-Roots of Composite Moduli II*

We improve estimates for the distribution of primitive λ-roots of a composite modulus q yielding an asymptotic formula for the number of primitive λ-roots in any interval I of length ∣I∣ ≫ q ...

Zhiyong Zheng, Todd Cochrane in Chinese Annals of Mathematics, Series B (2006)

Article

Upper Bounds on Character Sums with Rational Function Entries

We obtain formulae and estimates for character sums of the type $$ S{\left( {\chi ,f,p^{m} } \right)} = {\sum\nolimits_{x = 1}^{p^{m}...

Todd Cochrane, Chun Lei Liu, Zhi Yong Zheng in Acta Mathematica Sinica (2003)

Article

Upper bounds on a two-term exponential sum*

We obtain upper bounds for mixed exponential sums of the type $$S(\chi ,f,p^m ) = \sum\nolimits_{x = 1}^{p^n } {\chi (x)e} _{p^m } (ax...

Todd Cochrane, Zhiyong Zheng in Science in China Series A: Mathematics (2001)

Article

Small solutions of the congruencea ₁ x ₁ ² +a ₂ x ₂ ² +a ₃ x ₃ ² +a ₄ x ₄ ² ≡c(modp)

For any integersa ₁,a ₂,a ₃,a ₄ andc witha ₁ a ...

Todd Cochrane, Zheng Zhiyong in Acta Mathematica Sinica (1998)

Chapter

Bounds on complete exponential sums

We give a brief survey on complete exponential sums of the type S(g) = Σ_x e _p (g(x)), with g a polynomial in n variables over the finite field 픽 _...

Todd Cochrane in Analytic Number Theory (1996)

Chapter

Small Zeros of Quadratic Forms Modulo p, II

Let Q(x) = Q(x ₁ x _2,…, x _n) be a quadratic form with integer coefficients and p be an odd prime. Let µ=µ(Q,p) be minimal such that there is a...

Todd Cochrane in Analytic Number Theory (1990)

Article

Consecutive triples of sums of two squares

Todd Cochrane, Robert E. Dressler in Archiv der Mathematik (1987)