The partition function in arithmetic progressions
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چکیده
In celebration of G.E. Andrews' 60 th birthday.
منابع مشابه
On rainbow 4-term arithmetic progressions
{sl Let $[n]={1,dots, n}$ be colored in $k$ colors. A rainbow AP$(k)$ in $[n]$ is a $k$ term arithmetic progression whose elements have different colors. Conlon, Jungi'{c} and Radoiv{c}i'{c} cite{conlon} prove that there exists an equinumerous 4-coloring of $[4n]$ which is rainbow AP(4) free, when $n$ is even. Based on their construction, we show that such a coloring of $[4n]$...
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The arithmetic behavior of the partition function has been of great interest. For example, we have the famous Ramanujan congruences p(5n+ 4) ≡ 0 (mod 5), p(7n+ 5) ≡ 0 (mod 7), p(11n+ 6) ≡ 0 (mod 11) for every n ≥ 0. In a celebrated paper Ono [13] treated this type of congruence systematically. Combining Shimura’s theory of modular forms of half-integral weight with results of Serre on modular f...
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تاریخ انتشار 1998