On the mean squared modulus of a Dirichlet L-function over a short segment of the critical line
On the mean value of a sum analogous to character sums over short intervals
The main purpose of this paper is to study the mean value properties of a sum analogous to character sums over short intervals by using the mean value theorems for the Dirichlet L-functions, and to give some interesting asymptotic formulae.
On the mean value of Dedekind sum weighted by the quadratic Gauss sum
Various properties of classical Dedekind sums have been investigated by many authors. For example, Wenpeng Zhang, On the mean values of Dedekind sums, J. Théor. Nombres Bordx, 8 (1996), 429–442, studied the asymptotic behavior of the mean value of Dedekind sums, and H. Rademacher and E. Grosswald, Dedekind Sums, The Carus Mathematical Monographs No. 16, The Mathematical Association of America, Washington, D.C., 1972, studied the related properties. In this paper, we use the algebraic method to...
On the method of exponent pairs
On the number of Abelian groups of a given number.
On the numbers that are representable as the sum of two cubes.
On the order of
On the -adic continuation of the logarithmic derivative of certain hypergeometric functions
On the -free values of the polynomial
Let be a fixed integer. We study the asymptotic formula of , which is the number of positive integer solutions such that the polynomial is -free. We obtained the asymptotic formula of for all . Our result is new even in the case . We proved that , where is a constant depending on . This improves upon the error term obtained by G.-L. Zhou, Y. Ding (2022).
On the sphere problem.
One of the oldest problems in analytic number theory consists of counting points with integer coordinates in the d-dimensional ball. It is very easy to find a main term for the counting function, but the size of the error term is difficult to estimate (...).
On the sums
On the zeta function of monodromy of a polynomial map
On Zeros of Dirirchlet's L Series.
Optimal bounds for exponential sums in terms of discrepancy
Oscillations of Hecke eigenvalues at shifted primes.
In this paper, we are interested in exploring the cancellation of Hecke eigenvalues twisted with an exponential sums whose amplitude is √n at prime arguments.
in short intervals
For any sufficiently large real number , the interval contains at least one integer having at most two prime factors .
-adic estimates for exponential sums and the theorem of Chevalley-Warning
Petites solutions des congruences
Poincaré Series for GL (n): Fourier Expansion, Kloosterman Sums, and Algebreo-Geometric Estimates.
Primes in arithmetic progressions