A footnote to mean square value of DirichletL-series |
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Authors: | V V Rane |
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Institution: | 1. Department of Mathematics, The Institute of Science, 15, Madam Cama Road, 400 032, Bombay, India
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Abstract: | Following appropriate use of approximate functional equation for Hurwitz Zeta function, we obtain upper bounds for
} Here fors = σ + it, L(s,x) denotes DirichletL-series for character x(modq). In particular, we obtain S(1/2 +it) ≪q logqt + t5/8 q−1/8, which is an improvement in the range q |t| < q11/7, on hitherto best known result. This incidentally gives S(1/2+ it)≪ q log3q for |t|q9/5. |
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Keywords: | DirichletL-series |
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