Mean square value of exponential sums related to the representation of integers as sums of squares
Minimal -universality criteria may vary in size
In this note, we give simple examples of sets of quadratic forms that have minimal -universality criteria of multiple cardinalities. This answers a question of Kim, Kim, and Oh [KKO05] in the negative.
Mixed sums of squares and triangular numbers
Mixed sums of squares and triangular numbers. II.
Modular properties of theta-functions and representation of numbers by positive quadratic forms.