O součtech Gaussových
On a comparison of Gauss sums with products of Lagrange resolvents
On Bourgain's bound for short exponential sums and squarefree numbers
We use Bourgain's recent bound for short exponential sums to prove certain independence results related to the distribution of squarefree numbers in arithmetic progressions.
On characters of order p (mod p²)
On critical values of twisted Artin -functions
We give a simple proof that critical values of any Artin -function attached to a representation with character are stable under twisting by a totally even character , up to the -th power of the Gauss sum related to and an element in the field generated by the values of and over . This extends a result of Coates and Lichtenbaum as well as the previous work of Ward.
On Fleck quotients
On polynomial Gauss sums (mod Pⁿ), n ≥ 2
On Selberg's Eigenvalue Conjecture.
On Shioda's problem about Jacobi sums
On Shioda's problem about Jacobi sums II
On some Kloosterman sums.
On the determination of generalized Gauss sums
On the Dirichlet characters of polynomials in several variables
On the distribution of distances between the points of affine curves over finite fields.
On the distribution of inverses modulo p (II)
On the first power mean of -functions with the weight of general Kloosterman sums.
On the generalization of the D. H. Lehmer problem II
On the greatest prime divisor of quadratic sequences
On the hybrid mean value of Cochrane sums and generalized Kloosterman sums
On the -polygonal numbers and the mean value of Dedekind sums
For any positive integer , it is easy to prove that the -polygonal numbers are . The main purpose of this paper is, using the properties of Gauss sums and Dedekind sums, the mean square value theorem of Dirichlet -functions and the analytic methods, to study the computational problem of one kind mean value of Dedekind sums for -polygonal numbers with , and give an interesting computational formula for it.