Riedel M.R. Applications of the Mellin-Perron formula in number theory

Master thesis at University of Toronto. — Toronto: University of Toronto, 1996. — 147 p.A thesis submitted in conformity with the requirements for the degree of Master of Science Graduate Department of Computer Science University of Toronto 1996.
In a 1995 paper, P. Flajolet describes how to evaluate harmonic sums by the Mellin transform. We use his method to obtain an exact formula for consecutive approximations of the area of a fractal ornament delineated by three alternating Koch curves, and the average order of the number of lattice points inside a paraboloid, We define multiplicative self-similarity, i. e. a criterion for the existence of a Fourier series expansion of the solution to certain linear recurrences.
P. Flajolet’s method replaces an earlier, more complex method developed by H. Delange. This thesis applies P. Flajolet’s method to results previously proved by H. Delange’s, i. e. the evaluation of alternating digital sums, digital sums in periodic Cantor bases, asymptotic results for digital sums with arbitrary base/weight function combinations, and the error term of a sum related to the number of integers representable as a sum of three squares.