科研之友
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摘要
Recently, Duke and Jenkins have studied a certain family of modular forms f(k,m), which form a natural basis of the space of weakly holomorphic modular forms of weight k on SL2(Z). In particular, they prove that for all but at most left perpendicular k/12 right perpendicular + 1 values of m, the zeros of these functions all lie on the unit circle. Using a method of Kohnen, we observe that other than i, rho, these zeros are transcendental. In addition we observe that in the remaining cases there are at most finitely many algebraic zeros and examine the values of these algebraic zeros in a special case.
- 出版日期2014-3
