Displaying similar documents to “Enumeration of binary trees and universal types.”

On the number of prime factors of summands of partitions

Cécile Dartyge, András Sárközy, Mihály Szalay (2006)

Journal de Théorie des Nombres de Bordeaux

Similarity:

We present various results on the number of prime factors of the parts of a partition of an integer. We study the parity of this number, the extremal orders and we prove a Hardy-Ramanujan type theorem. These results show that for almost all partitions of an integer the sequence of the parts satisfies similar arithmetic properties as the sequence of natural numbers.

A study of the mean value of the error term in the mean square formula of the Riemann zeta-function in the critical strip 3 / 4 ≤ σ < 1

Yuk-Kam Lau (2006)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let E σ ( T ) be the error term in the mean square formula of the Riemann zeta-function in the critical strip 1 / 2 < σ < 1 . It is an analogue of the classical error term E ( T ) . The research of E ( T ) has a long history but the investigation of E σ ( T ) is quite new. In particular there is only a few information known about E σ ( T ) for 3 / 4 < σ < 1 . As an exploration, we study its mean value ∫ 1 T E σ ( u ) d u . In this paper, we give it an Atkinson-type series expansion and explore many of its properties as a function of T .

Ternary quadratic forms with rational zeros

John Friedlander, Henryk Iwaniec (2010)

Journal de Théorie des Nombres de Bordeaux

Similarity:

We consider the Legendre quadratic forms ϕ a b ( x , y , z ) = a x 2 + b y 2 - z 2 and, in particular, a question posed by J–P. Serre, to count the number of pairs of integers 1 ≤ a ≤ A , 1 ≤ b ≤ B , for which the form ϕ a b has a non-trivial rational zero. Under certain mild conditions on the integers a , b , we are able to find the asymptotic formula for the number of such forms.