Introduction In 1903 Voronoi [42] postulated the existence of explicit formulas for sums of the form () n≥1 an f (n) , for any “arithmetically interesting” sequence of coefficients (an )n≥1 and every f in a large class of test functions, including characteristic functions of bounded intervals. He actually established such a formula when an = d(n) is the number of positive divisors of n [43]. He also asserted a formula for () an = #{(a, b) ∈ Z2 | Q(a, b) = n} , where Q denotes a positive definite integral quadratic form [44]; .
