Arithmetic and analytic aspects of values of L-functions [HBNI Th240]

By: Material type: TextTextLanguage: English Publication details: Chennai The Institute of Mathematical Sciences 2024Description: iv, 134pSubject(s): Online resources: Dissertation note: Ph.D HBNI 2024 Summary: The central theme of this thesis is to study some analytic and arithmetic properties of values of L-functions at “special points”. The values of L-functions encode a lot of arithmetic data and are at the heart of several deep mysteries. The Riemann hypothesis which predicts that all non-trivial zeros of the Riemann zeta function lie on the line ℜ(s) = 1/2 is one such enigma. For a non-trivial Dirichlet character χ, it is expected that L(s, χ) does not vanish at 1/2. Though this problem is still wide open, a lot of progress has been made in recent years.
Item type: THESIS & DISSERTATION
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IMSc Library HBNI Th240 (Browse shelf(Opens below)) Link to resource Not For Loan 77925

Ph.D HBNI 2024

The central theme of this thesis is to study some analytic and arithmetic properties of values of L-functions at “special points”. The values of L-functions encode a lot of arithmetic data and are at the heart of several deep mysteries. The Riemann hypothesis which predicts that all non-trivial zeros of the Riemann zeta function lie on the line ℜ(s) = 1/2 is one such enigma. For a non-trivial Dirichlet character χ, it is expected that L(s, χ) does not vanish at 1/2. Though this problem is still wide open, a lot of progress has been made in recent years.

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The Institute of Mathematical Sciences, Chennai, India