Nov 24, 2010 · Gauss sums and exponential sums in general are particularly useful for determining the size of certain algebraic varieties in finite fields or even in general abelian groups.

Gauss sums with respect to more general characters have a similar relationship to actions of the Galois group.

From here you can use reduction properties of the quadratic Gauss sum and the Chinese Remainder Theorem to prove the even cases. There is no general formula for a generalized …

Oct 27, 2016 · How to calculate Gauss sum? Ask Question Asked 9 years, 2 months ago Modified 9 years ago

Nov 28, 2024 · The generalized quadratic Gauss sums has several properities, which can be found https://en.wikipedia.org/wiki/Quadratic_Gauss_sum. My confusion is that what the …

Jul 20, 2023 · 0 This may be a rather silly question, but I found myself thinking about the famous anecdote of Gauss summing from 1 to 100 in school, where he sums $$1+100=101, …

EDIT Since you're only interested in the "Gaussian" method of summing this series, I suggest you take a look at this Wikipedia article on Arithmetic progression. It shows how you can use this …

Mar 16, 2019 · I am given a non-trivial homomorphism $\chi : \left (\mathbb {Z} / p\mathbb {Z} \right)^\times \rightarrow \mathbb {C}^\times$, p is prime, and $\zeta$ is a primitive p-th root of …

Feb 28, 2024 · Gauss sum in character theory Ask Question Asked 1 year, 9 months ago Modified 1 year, 7 months ago

Aug 18, 2023 · I think it is easier to go from the RHS to the LHS. The RHS is $$ \sum_ {m=1}^ {N} \chi (m)\left ( \sum_ {n=-\infty}^ {+\infty}\omega^ {mn}e^ {\frac {-n^2\pi x} {N}} \right) = \sum_ {n …