Partial sums of the Möbius function in arithmetic progressions assuming GRH
نویسندگان
چکیده
منابع مشابه
Bounding sums of the Möbius function over arithmetic progressions
Let M(x) = ∑ 1≤n≤x μ(n) where μ is the Möbius function. It is well-known that the Riemann Hypothesis is equivalent to the assertion that M(x) = O(x1/2+ ) for all > 0. There has been much interest and progress in further bounding M(x) under the assumption of the Riemann Hypothesis. In 2009, Soundararajan established the current best bound of M(x) √ x exp ( (log x)(log log x) ) (setting c to 14, ...
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3 Proof of Theorem 1 9 3.1 Estimation of the g1 term. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.2 Estimation of the g3 term. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.3 Estimation of the g2 term. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.4 Putting everything together. . . . . . . . . . . . . . . . . . . . . ....
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ژورنال
عنوان ژورنال: Functiones et Approximatio Commentarii Mathematici
سال: 2013
ISSN: 0208-6573
DOI: 10.7169/facm/2013.48.1.6