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VIDEO LIBRARY |
À.A.Karatsuba's 80th Birthday Conference in Number Theory and Applications
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Zeros-distribution of the Riemann zeta-function and universality A. P. Laurinčikas Institute of Mathematics and Informatics, Vilnius University, Vilnius |
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Abstract: In 1975, S.M. Voronin discovered the universality property of the zeta-function We consider the universality of We suppose that $$ \mathop{\sum_{\gamma_{l},\gamma_{k} \le T}}\limits_{|\gamma_{l}-\gamma_{k}|<{c\over \log T}}1\,\ll\,T\log T, \quad T\to\infty, $$ with a certain constant Let $D=\bigl\{s\in \mathbb{C}: \tfrac{1}{2}<\sigma<1\bigr\}$, Theorem. Suppose that the weak Montgomery conjecture is true. Let $$ \liminf_{N\to\infty} \frac{1}{N} \# \left\{ 1\leqslant k\leqslant N: \sup_{s\in K} |\zeta(s+i\gamma_k h)-f(s)|<\varepsilon\right\}>0. $$ In the report, the approximation of analytic functions by [1] H.L. Montgomery, The pair correlation of zeros of the zeta function. In: Analytic Number Theory, (St. Louis Univ., 1972), H.G. Diamond (ed.), Proc. Sympos. Pure Math., Vol. XXIV, Amer. Math. Soc. Providence, 1973. P. 181 – 193. Language: English |