On the divisor problem: Moments of Δ(x) over short intervals
Werner Georg Nowak (2003)
Acta Arithmetica
Christian Ballot, Florian Luca (2007)
Acta Arithmetica
R. Balasubramanian, K. Ramachandra, M. Subbarao (1988)
Acta Arithmetica
Aleksandar Ivic (1992)
Monatshefte für Mathematik
Wenguang Zhai (2008)
Acta Arithmetica
H. Maier, A. Sankaranarayanan (2005)
Acta Arithmetica
Juanjo Rué, Paulius Šarka, Ana Zumalacárregui (2013)
Journal de Théorie des Nombres de Bordeaux
We study the logarithm of the least common multiple of the sequence of integers given by . Using a result of Homma [5] on the distribution of roots of quadratic polynomials modulo primes we calculate the error term for the asymptotics obtained by Cilleruelo [3].
Hershy Kisilevsky, Francesco Pappalardi (1995)
Acta Arithmetica
A. Smati, J. Wu (1997)
Publications de l'Institut Mathématique
Bahman Saffari, R. C. Vaughan (1977)
Annales de l'institut Fourier
As promised in the first paper of this series (Ann. Inst. Fourier, 26-4 (1976), 115-131), these two articles deal with the asymptotic distribution of the fractional parts of where is an arithmetical function (namely , , ) and is an integer (or a prime order) running over the interval . The results obtained are rather sharp, although one can improve on some of them at the cost of increased technicality. Number-theoretic applications will be given later on.
Karl K. Norton (1994)
Acta Arithmetica
Kátai, Imre, Subbarao, M.V. (2005)
Mathematica Pannonica
Yaming Lu, Yuan Yi (2010)
Acta Arithmetica
Tingting Wang (2012)
Acta Arithmetica
Wenpeng Zhang (2000)
Acta Arithmetica
Hubert Delange (1993)
Monatshefte für Mathematik
Christopher Hooley (1974)
Journal für die reine und angewandte Mathematik
Bencherif, Farid, Robin, Guy (1994)
Publications de l'Institut Mathématique. Nouvelle Série
Jun Furuya, Wenguang Zhai (2006)
Acta Arithmetica
Jun Furuya, Wenguang Zhai (2008)
Acta Arithmetica