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Zeros of derivatives of Riemann's ξ-function on the critical line

✍ Scribed by Brian Conrey


Publisher
Elsevier Science
Year
1983
Tongue
English
Weight
921 KB
Volume
16
Category
Article
ISSN
0022-314X

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On the Zeros of Higher Derivatives of Ha
✍ Kohji Matsumoto; Yoshio Tanigawa 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 137 KB

Let k be any positive integer and N 0, k (T ) the number of the zeros in the interval (0, T ) of Z (k) (t), the kth derivative of Hardy's Z-function. We prove an inequality for N 0, k (T) (Theorem 1), and also prove that it can be replaced by the equality under the Riemann hypothesis (Theorem 2). Th