A character-sum estimate and applications
A generalization of Bombieri's prime number theorem to algebraic number fields
A hybrid mean value involving two-term exponential sums and polynomial character sums
Let be a positive integer. For any integers and , the two-term exponential sum is defined by , where . In this paper, we use the properties of Gauss sums and the estimate for Dirichlet character of polynomials to study the mean value problem involving two-term exponential sums and Dirichlet character of polynomials, and give an interesting asymptotic formula for it.
A hybrid mean value of the Dedekind sums
The main purpose of this paper is to use the M. Toyoizumi's important work, the properties of the Dedekind sums and the estimates for character sums to study a hybrid mean value of the Dedekind sums, and give a sharper asymptotic formula for it.
A mean value estimate for real character sums
A multidimensional version of a result of Davenport-Erdős.
A note on the Dirichlet characters of polynomials
A problem on semicubical powers
A subconvexity bound for Hecke L-functions
Abschätzung trigonometrischer Summen.
An upper bound for the number of solutions of a system of congruences
Average r-rank Artin conjecture
Let Γ ⊂ ℚ * be a finitely generated subgroup and let p be a prime such that the reduction group Γₚ is a well defined subgroup of the multiplicative group ₚ*. We prove an asymptotic formula for the average of the number of primes p ≤ x for which [ₚ*:Γₚ] = m. The average is taken over all finitely generated subgroups , with and , with a range of uniformity for every i = 1,...,r. We also prove an asymptotic formula for the mean square of the error terms in the asymptotic formula with a similar...
Bounds for automorphic L-functions.
Bounds for exponential sums
Character Sums and Primitive Roots in Algebraic Number Fields.
Character sums and products of factorials modulo
In this paper, we apply character sum estimates to study products of factorials modulo .
Character sums and Ramsey properties of generalized Paley graphs.
Character sums in complex half-planes
Let be a finite subset of an abelian group and let be a closed half-plane of the complex plane, containing zero. We show that (unless possesses a special, explicitly indicated structure) there exists a non-trivial Fourier coefficient of the indicator function of which belongs to . In other words, there exists a non-trivial character such that .
Cohomologie des fonctions
Density theorems for exceptional eigenvalues of the Laplacian for congruence groups