Annales Academić Scientiarum Fennicć
Mathematica
Volumen 33, 2008, 549-560

OMEGA RESULT FOR THE ERROR TERM IN THE MEAN SQUARE FORMULA FOR DIRICHLET L-FUNCTIONS

Yuk-Kam Lau and Kai-Man Tsang

University of Hong Kong, Department of Mathematics
Pokfulam Road, Hong Kong; yklau 'at' maths.hku.hk

University of Hong Kong, Department of Mathematics
Pokfulam Road, Hong Kong; kmtsang 'at' maths.hku.hk

Abstract. Let q be a positive integer and let E(q,x) denote the error term in the asymptotic formula for the mean value \sum_{\chi mod q} \int₀^x|L(1/2 + it,\chi)|² dt. We obtain in this paper an \Omega-result for E(q,x), which is an extension of the corresponding \Omega-result for the Riemann zeta-function.

2000 Mathematics Subject Classification: Primary 11M06.

Key words: Mean-square formula, Atkinson's formula, omega-results.

Reference to this article: Y.-K. Lau and K.-M. Tsang: Omega result for the error term in the mean square formula for Dirichlet L-functions. Ann. Acad. Sci. Fenn. Math. 33 (2008), 549-560.

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