On sets of weak uniform distribution
On shifted primes
On short sums of certain multiplicative functions.
On Siegel Zeros of Hecke-Landau Zeta-Functions.
On Sieve method and Goldbach problem
On sign-changes in the remainder-term of the prime-number formula, II
On sign-changes in the remainder-term of the prime-number formula, I
On sign-changes in the remainder-term of the prime-number formula, IV
On sign-changes in the remainder-term of the prime-number formula, III
On small eigenvalues of the Laplacian for ...(q). .
On smooth integers in short intervals under the Riemann Hypothesis
On some complex explicit formulae connected with the Mobius function. II
On some complex explicit formulae connected with the Mobius function. I
On Some Connections Between Zeta-Zeros and Square-Free Integers.
On some divisor problems
On some estimates involving the number of prime divisors of an integer
On some exponential sums involving divisor functions.
On some Extremal Problems of Landau
2000 Mathematics Subject Classification: Primary: 42A05. Secondary: 42A82, 11N05.The prime number theorem with error term presents itself as &pi'(x) = ∫2x [dt/ logt] + O ( x e- K logL x). In 1909, Edmund Landau provided a systematic analysis of the proof seeking better values of L and K. At a key point of his 1899 proof de la Vallée Poussin made use of the nonnegative trigonometric polynomial 2/3 (1+cos x)2 = 1+4/3 cosx +1/3 cos2x. Landau considered more general positive definite nonnegative...
On some inequalities concerning .
On some mean value results for the zeta-function in short intervals
Let denote the error term in the Dirichlet divisor problem, and let E(T) denote the error term in the asymptotic formula for the mean square of |ζ(1/2+it)|. If E*(t) := E(t) - 2πΔ*(t/(2π)) with Δ*(x) = -Δ(x) + 2Δ(2x) - 1/2Δ(4x) and , then we obtain a number of results involving the moments of |ζ(1/2+it)| in short intervals, by connecting them to the moments of E*(T) and R(T) in short intervals. Upper bounds and asymptotic formulae for integrals of the form ∫T2T(∫t-Ht+H |ζ(1/2+iu|2 duk dtare...