Displaying similar documents to “A Terr algorithm for computations in the infrastructure of real-quadratic number fields”

Explicit lower bounds for linear forms in two logarithms

Nicolas Gouillon (2006)

Journal de Théorie des Nombres de Bordeaux

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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 .

Ternary quadratic forms with rational zeros

John Friedlander, Henryk Iwaniec (2010)

Journal de Théorie des Nombres de Bordeaux

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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.

Perfect powers in the summatory function of the power tower

Florian Luca, Diego Marques (2010)

Journal de Théorie des Nombres de Bordeaux

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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 .

Oscillation of Mertens’ product formula

Harold G. Diamond, Janos Pintz (2009)

Journal de Théorie des Nombres de Bordeaux

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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.