ESTIMATES OF θ ( x ; k , l ) FOR LARGE VALUES OF x PIERRE
نویسنده
چکیده
We extend a result of Ramaré and Rumely, 1996, about the Chebyshev function θ in arithmetic progressions. We find a map ε(x) such that | θ(x; k, l)− x/φ(k) |< xε(x) and ε(x) = O ( 1 lna x ) (∀a > 0), whereas ε(x) is a constant. Now we are able to show that, for x > 1531, | θ(x; 3, l)− x/2 |< 0.262 x lnx and, for x > 151, π(x; 3, l) > x 2 lnx .
منابع مشابه
Estimates of Θ(x; K, L) for Large Values of X
We extend a result of Ramaré and Rumely, 1996, about the Chebyshev function θ in arithmetic progressions. We find a map ε(x) such that | θ(x; k, l)− x/φ(k) |< xε(x) and ε(x) = O ( 1 lna x ) (∀a > 0), whereas ε(x) is a constant. Now we are able to show that, for x > 1531, | θ(x; 3, l)− x/2 |< 0.262 x lnx and, for x > 151, π(x; 3, l) > x 2 lnx .
متن کاملk , l ) FOR LARGE VALUES OF x
We extend a result of Ramaré & Rumely, 1996 [3] about Chebyshev function θ in arithmetic progressions. We find a map ε(x) such that | θ(x; k, l) − x/φ(k) |< xε(x) and ε(x) = O ( 1 lna x ) (∀a > 0) whereas ε(x) is a constant in [3]. Now we are able to show that | θ(x; 3, l)− x/2 |< 0.262 x lnx and, for x > 151, π(x; 3, l) > x 2 lnx .
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