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PDF-2JANHENDRIKBRUINIERANDKENONOWeobtainanewformulaforp(n).AnsweringQuesti PDF document

24Q1n11qnnoteqe2izthroughoutandthequasimodularEisensteinseries12E2z1241Xn1XdjndqnTothisendwede nethe06weight2meromorphicmodularformFzby13Fz1 2E2z2E22z3E23z6

24Q1n=1(1qn)(note.q:=e2izthroughout)andthequasimodularEisensteinseries(1.2)E2(z):=1241Xn=1Xdjndqn:Tothisend wede nethe0(6)weight-2meromorphicmodularformF(z)by(1.3)F(z):=1 2E2(z)2E2(2z)3E2(3z)+6

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