Arithmetic Properties of Non-harmonic Weak Maass Forms
نویسندگان
چکیده
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 forms modulo `, he showed that for any prime ` ≥ 5 there exist infinitely many non-nested arithmetic progressions An+B such that for every n ≥ 0, p(An+B) ≡ 0 (mod `). Now consider the function
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