Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp0112579w10h
 Title: On admissible integers of cubic forms Authors: Diaconu, Simona Advisors: Sarnak, Peter Department: Mathematics Class Year: 2019 Abstract: In this paper, we are mainly concerned with the form f(X,Y,Z)=X$$^{3}$$+Y$$^{3}$$+Z$$^{3}$$ and more precisely, what integers this cubic can represent and which regions of R$$^{3}$$ can cover at least one solution for almost all the potential integers that could be represented by it. We show first that for a family of regions in R$$^3$$ to cover almost all the admissible integers of any diagonal cubic form, the number of solutions in each region must grow faster than any linear function, and next we choose a potential family for the cubic f(X, Y, Z). URI: http://arks.princeton.edu/ark:/88435/dsp0112579w10h Type of Material: Princeton University Senior Theses Language: en Appears in Collections: Mathematics, 1934-2020