Hecke Operators and Zeros of Modular Forms

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• 作者：Victor Manuel Aricheta ; Richell Celeste…
• 刊名：Bulletin of the Malaysian Mathematical Sciences Society
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：39
• 期：3
• 页码：1249-1257
• 全文大小：434 KB
• 刊物类别：Mathematics, general; Applications of Mathematics;
• 刊物主题：Mathematics, general; Applications of Mathematics;
• 出版者：Springer Singapore
• ISSN：2180-4206
• 卷排序：39

文摘

Let \(T_n\) be the nth Hecke operator and \(f \in M_k\) be nonzero. We show that if the eigenvalues of \(T_n\) are distinct and nonzero for some \(n\in \mathbb {N}\), then f is an eigenform if and only if f and \(T_nf\) have the same zeros (counting multiplicity) in \(\mathbb {C} \cup \{\infty \}\). For \(k \le 26\), we use this result to obtain properties of f given the number of zeros common to f and \(T_nf\).KeywordsHecke operatorsModular formsZeros of modular forms