Zeros of L-functions

Ze-Li Dou () and Qiao Zhang ()
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Ze-Li Dou: Texas Christian University, Department of Mathematics
Qiao Zhang: Texas Christian University, Department of Mathematics

Chapter Chapter 4 in Six Short Chapters on Automorphic Forms and L-functions, 2012, pp 57-75 from Springer

Abstract: Abstract In Chapter 1, we introduced the L-functions of modular forms and indicated briefly how useful they are in our study of arithmetic problems. In fact, the converse theorem of Weil asserts that an L-function, together with its twists, uniquely determines the modular form itself. Hence the study of modular forms can be largely reduced to that of their L-functions. Since L-functions are simply certain complex analytic functions, we can employ our familiar theory of complex analysis to study them, thereby facilitating our study of arithmetic problems for modular forms themselves.

Keywords: Modular Form; Critical Line; Riemann Zeta Function; Random Matrix Theory; Riemann Hypothesis (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-3-642-28708-4_4

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