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Monday, October 19, 2015 - 14:30 to 15:30
Prof. U. K. Ananadavardhanan
IIT, Mumbai
  • Title: The sign of the Gauss sum  
  • Abstract: One way to understand the connections between two different structures is to mix the two and to observe the resulting object! This is what Gauss did when he started his study of what is now called a Gauss sum. A Gauss sum is a mix of an additive map with a multiplicative map, where both the operations are done modulo a fixed prime number. It is not hard to see that the value of the most interesting case of the Gauss sum, appropriately normalized, is either $\pm 1$ or $\pm \imath$. However, Gauss proved in 1805, apparently it took four years for him to do this (!), that it is always $1$ or $\imath$. We'll discuss this result of Gauss and some of its generalizations.

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