On the variance of sums of divisor functions in short intervals
Copyright policy )On the variance of sums of divisor functions in short intervals
Given a positive integer n n the k k -fold divisor function d k ( n ) d_k(n) equals the number of ordered k k -tuples of positive integers whose product equals n n . In this article we study the variance of sums of d k ( n ) d_k(n) in short intervals and establish asymptotic formulas for the variance of sums of d k ( n ) d_k(n) in short intervals of certain lengths for k = 3 k=3 and for k ≥ 4 k \ge 4 under the assumption of the Lindelöf hypothesis.
- Tel Aviv University Israel
- Queen Mary University of London United Kingdom
- Royal Institute of Technology Sweden
Matematik, Mathematics - Number Theory, \(k\)-fold divisor function, Lindelöf hypothesis, \(\zeta (s)\) and \(L(s, \chi)\), FOS: Mathematics, Asymptotic results on arithmetic functions, variance of sums, Number Theory (math.NT), Mathematics
Matematik, Mathematics - Number Theory, \(k\)-fold divisor function, Lindelöf hypothesis, \(\zeta (s)\) and \(L(s, \chi)\), FOS: Mathematics, Asymptotic results on arithmetic functions, variance of sums, Number Theory (math.NT), Mathematics
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