Displaying similar documents to “Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions.”

Oscillation of Mertens’ product formula

Harold G. Diamond, Janos Pintz (2009)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Mertens’ product formula asserts that ∏ p ≤ x 1 - 1 p log x → e - γ as x → ∞ . Calculation shows that the right side of the formula exceeds the left side for 2 ≤ x ≤ 10 8 . It was suggested by Rosser and Schoenfeld that, by analogy with Littlewood’s result on π ( x ) - li x , this and a complementary inequality might change their sense for sufficiently large values of x . We show this to be the case.

Perfect powers in the summatory function of the power tower

Florian Luca, Diego Marques (2010)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let ( a n ) n ≥ 1 be the sequence given by a 1 = 1 and a n = n a n - 1 for n ≥ 2 . In this paper, we show that the only solution of the equation a 1 + ⋯ + a n = m l is in positive integers l > 1 , m and n is m = n = 1 .

Explicit lower bounds for linear forms in two logarithms

Nicolas Gouillon (2006)

Journal de Théorie des Nombres de Bordeaux

Similarity:

We give an explicit lower bound for linear forms in two logarithms. For this we specialize the so-called Schneider method with multiplicity described in []. We substantially improve the numerical constants involved in existing statements for linear forms in two logarithms, obtained from Baker’s method or Schneider’s method with multiplicity. Our constant is around 5 . 10 4 instead of 10 8 .