On a conjecture of J. E. Littlewood.
On a Conjecture of Littlewood Concerning Exponentials Sums, II
On a Monotonic Trigonometric Sum.
On a positive sine sum
On a Problem of Best Uniform Approximation and a Polynomial Inequality of Visser
In this paper, a generalization of a result on the uniform best approximation of α cos nx + β sin nx by trigonometric polynomials of degree less than n is considered and its relationship with a well-known polynomial inequality of C. Visser is indicated.
On a sum of Vinogradov
On an infinite linear combination of partial sums of Fourier series
On Baica's trigonometric identity.
On Bernstein's Inequality and Kahane's Ultraflat Polynomials.
On cosine polynomials corresponding to sets of integers
On Fourier coefficients of class .
On Kahane's ultraflat polynomials
On polynomials with simple trigonometric formulas.
On some constants in simultaneous approximation.
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 the best constants in some inequalities for entire functions of exponential type
On the boundedness of the norms of trigonometric polynomials and their application to summation methods of Fourier series.
On the Constant in the Littlewood Problem.
On the convergence of moments in the CLT for triangular arrays with an application to random polynomials
We give a proof of convergence of moments in the Central Limit Theorem (under the Lyapunov-Lindeberg condition) for triangular arrays, yielding a new estimate of the speed of convergence expressed in terms of νth moments. We also give an application to the convergence in the mean of the pth moments of certain random trigonometric polynomials built from triangular arrays of independent random variables, thereby extending some recent work of Borwein and Lockhart.
On the distribution of zeros of exponential polynomials