Choosing Smoothing Parameters For Exponential Smoothing: Minimizing Sums Of Squared Versus Sums Of Absolute Errors

Choosing Smoothing Parameters For Exponential Smoothing: Minimizing Sums Of Squared Versus Sums Of Absolute Errors

DiophantineMethods for Exponential Sums, and Exponential Sums for Diophantine Problems

Recent developments in the theory and application of the HardyLittlewood method are discussed, concentrating on aspects associated with diagonal diophantine problems. Recent efficient differencing methods for estimating mean values of exponential sums are described first, concentrating on developments involving smooth Weyl sums. Next, arithmetic variants of classical inequalities of Bessel and ...

on direct sums of baer modules

the notion of baer modules was defined recently

Exponential Sums

where we in introduce the standard notation e(x) = exp(2πix). Question 1.1. What is the magnitude of | ∑ x∈S e(x)|? By the trivial bound, we find that | ∑ x∈S e(x)| ≤ N , with equality whenever the terms are all equal. One can of course make the sum much smaller–simply sum the Nth roots of unity. In between these two extremes–completely in phase and maximally out of phase–we should consider wha...

Inequalities for Exponential Sums

We study the classes