Displaying similar documents to “Lindelöf representations and (non-)holonomic sequences.”

A study of the mean value of the error term in the mean square formula of the Riemann zeta-function in the critical strip 3 / 4 ≤ σ < 1

Yuk-Kam Lau (2006)

Journal de Théorie des Nombres de Bordeaux

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Let E σ ( T ) be the error term in the mean square formula of the Riemann zeta-function in the critical strip 1 / 2 < σ < 1 . It is an analogue of the classical error term E ( T ) . The research of E ( T ) has a long history but the investigation of E σ ( T ) is quite new. In particular there is only a few information known about E σ ( T ) for 3 / 4 < σ < 1 . As an exploration, we study its mean value ∫ 1 T E σ ( u ) d u . In this paper, we give it an Atkinson-type series expansion and explore many of its properties as a function of T .

Special values of multiple gamma functions

William Duke, Özlem Imamoḡlu (2006)

Journal de Théorie des Nombres de Bordeaux

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We give a Chowla-Selberg type formula that connects a generalization of the eta-function to GL ( n ) with multiple gamma functions. We also present some simple infinite product identities for certain special values of the multiple gamma function.