New Forms and Old Forms

Xueli Wang () and Dingyi Pei ()
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Xueli Wang: South China Normal University, Department of Mathematics
Dingyi Pei: Guangzhou University, Institute of Mathematics and Information Science

Chapter Chapter 6 in Modular Forms with Integral and Half-Integral Weights, 2012, pp 153-204 from Springer

Abstract: Abstract Let N, k positive integers, χ a character modulo N. We know that the Hecke operators T(n),(n, N) = 1 can be diagonalized simultaneously in the space S(N,k,χ). On the other hand, if f is an eigenfunction of all Hecke operators T(n), then L(s, f) has an Euler product. So we want to ask the following question: Can all Hecke operators T(n) be diagonalized simultaneously in the space S(N, k, χ).

Keywords: Positive Integer; Modular Form; Prime Divisor; Cusp Form; Multiplicative Function (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-3-642-29302-3_6

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