This project concerns one of the most important
tools in analytic number theory, namely summation formulas. Particular
attention will be paid to Euler-Maclaurin formula, Poisson summation formula
and Voronoi summation formula. The main application will be to the study of summation
formulas for the hyperbola and to Dirichlet's divisor problem. This problem has
a long and rich history and concerns with investigation of one of the most
"elementary" arithmetic functions in number theory - the divisor
function d(n), which counts the number of positive divisors of a natural number
"n". The expected outcome of the project is an
account on the theory of summation formulas and the main techniques used in some
of the results on Dirichlet's divisor problem. Furthermore, the project may
include investigations on divisor problem in arithmetic progressions.
For more details on the project, check
here.
Obs! För GU-studenter räknas projektet som ett projekt i Matematik (MMG900/MMG910).
Projektkod MVEX01-18-19
Gruppstorlek 3-5
Examinator Maria Roginskaya, Marina Axelson-Fisk
Institution Matematiska vetenskaper