All Questions

Good evening. I am writing a paper on complex analysis, and as a corollary (of my work and others'), I believe that I have managed to deduce the following result. Proposition: Let $n_1 < n_2 \cdots ...

I am struggling with 1.11 exercise from the George Shakan "Discrete Fourier Transform". Let $A \subset \mathbb{Z}/q\mathbb{Z}$ be any set not containing zero with $|A|>\sqrt2q^{5/8}$. ...

I wish to show that the Fourier pseudorandomness is insufficient to count the number of 4-term arithmetic progression. Let $A \subset \mathbb{Z}/N\mathbb{Z}$ be a subset of a cyclic group $\mathbb{Z}/...

For any $c \in \mathbb{F}_2^n$ define $\sigma_c: \mathbb{F}_2^n \to \mathbb{F}_2$ the quadratic polynomial defined for $v = (v_1,v_2,...,v_n)$ by: $$ \sigma_c (v) = \sum_{i=1}^n v_iv_{i+1} + c_iv_i $...

Roth first proved that any subset of the integers with positive density contains a three term arithmetic progression in 1953. Since then, many other proofs have emerged (I can think of eight off the ...