Displaying similar documents to “Asymptotic bounds for bipartite Ramsey numbers.”

Complete solutions of a family of cubic Thue equations

Alain Togbé (2006)

Journal de Théorie des Nombres de Bordeaux

Similarity:

In this paper, we use Baker’s method, based on linear forms of logarithms, to solve a family of Thue equations associated with a family of number fields of degree 3. We obtain all solutions to the Thue equation Φ n ( x , y ) = x 3 + ( n 8 + 2 n 6 - 3 n 5 + 3 n 4 - 4 n 3 + 5 n 2 - 3 n + 3 ) x 2 y - ( n 3 - 2 ) n 2 x y 2 - y 3 = ± 1 , for n 0 .

A new lower bound for ( 3 / 2 ) k

Wadim Zudilin (2007)

Journal de Théorie des Nombres de Bordeaux

Similarity:

We prove that, for all integers k exceeding some effectively computable number  K , the distance from ( 3 / 2 ) k to the nearest integer is greater than 0 . 5803 k .

On a conjecture of Mąkowski and Schinzel concerning the composition of the arithmetic functions σ and ϕ

A. Grytczuk, F. Luca, M. Wójtowicz (2000)

Colloquium Mathematicae

Similarity:

For any positive integer n let ϕ(n) and σ(n) be the Euler function of n and the sum of divisors of n, respectively. In [5], Mąkowski and Schinzel conjectured that the inequality σ(ϕ(n)) ≥ n/2 holds for all positive integers n. We show that the lower density of the set of positive integers satisfying the above inequality is at least 0.74.

On the mean values of an analytic function.

G. S. Srivastava, Sunita Rani (1992)

Annales Polonici Mathematici

Similarity:

Let f(z), z = r e i θ , be analytic in the finite disc |z| < R. The growth properties of f(z) are studied using the mean values I δ ( r ) and the iterated mean values N δ , k ( r ) of f(z). A convexity result for the above mean values is obtained and their relative growth is studied using the order and type of f(z).