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Results tagged with additive-combinatorics
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user 38104
Questions on the subject additive combinatorics, also known as arithmetic combinatorics, such as questions on: additive bases, sum sets, inverse sum set theorems, sets with small doubling, Sidon sets, Szemerédi's theorem and its ramifications, Gowers uniformity norms, etc. Often combined with the top-level tags nt.number-theory or co.combinatorics. Some additional tags are available for further specialization, including the tags sumsets and sidon-sets.
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Asymptotic formula for the number of ways to write a number as the sum of $k$ triangular num...
Use circle method detect the condition $N=\sum_{i=1}^k \frac{m_i(m_i+1)}{2}$ to derive
$r(N)=\int_0^1 f^k(\alpha) e(-N\alpha)$, where $f(\alpha)=\sum_{n\leq N} e(\alpha \frac{m_i(m_i+1)}{2} )=\int_ …