Trace formulas applied to the Riemann $$\zeta$$-function.(English)Zbl 1440.11086

Kuru, Şengül (ed.) et al., Integrability, supersymmetry and coherent states. A volume in honour of Professor Véronique Hussin. In part selected contributions from the 6th international workshop on new challenges in quantum mechanics: integrability and supersymmetry, Valladolid, Spain, June 27–30, 2017. Cham: Springer. CRM Ser. Math. Phys., 231-253 (2019).
Summary: We use a spectral theory perspective to reconsider properties of the Riemann zeta function. In particular, new integral representations are derived and used to present its value at odd positive integers.
For the entire collection see [Zbl 1421.81004].

MSC:

 11F72 Spectral theory; trace formulas (e.g., that of Selberg) 11M26 Nonreal zeros of $$\zeta (s)$$ and $$L(s, \chi)$$; Riemann and other hypotheses 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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