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Displaying similar documents to “Special values of multiple gamma functions”

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 .

Almost powers in the Lucas sequence

Yann Bugeaud, Florian Luca, Maurice Mignotte, Samir Siksek (2008)

Journal de Théorie des Nombres de Bordeaux

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The famous problem of determining all perfect powers in the Fibonacci sequence ( F n ) n ≥ 0 and in the Lucas sequence ( L n ) n ≥ 0 has recently been resolved []. The proofs of those results combine modular techniques from Wiles’ proof of Fermat’s Last Theorem with classical techniques from Baker’s theory and Diophantine approximation. In this paper, we solve the Diophantine equations L n = q a y p , with a > 0 and p ≥ 2 , for all primes q < 1087 and indeed for all but 13 primes q < 10 6 . Here the strategy of [] is not sufficient due to the sizes...