## Algebra Seminar

Friday, February 16, 2018
1:20 PM - 4:00 PM (ET)
Exley Science Center Tower ESC 618
Event Type
Seminar/Colloquium
Contact
Canalia, Caryn
2182
Abstract:  For every positive integer n, let g(n) be the smallest integer such that if an integral quadratic form in n variables can be written as a sum of squares of integral linear forms, then it can be written as a sum of g(n) squares of integral linear forms. As a generalization of Lagranges Four-Square Theorem, Mordell (1930) showed that g(2) = 5 and later that year Ko (1930) showed that g(n) = n + 3 when n 5. More than sixty years later, M.-H. Kim and B.-K. Oh (1996) showed that g(6) = 10, and later (2005) they showed that the growth of g(n) is at most an exponential of n. In this talk, I will discuss a recent improvement of Kim and Oh's result showing that the growth of g(n) is at most an exponential of $\sqrt{n}$.