/pdf/argument-dzeta-funktsii-rimana-the-argument-of-the-riemann-33fff694nk.pdf

Аргумент дзета-функции Римана@@@The argument of the Riemann zeta function

/pdf/povedenie-argumenta-dzeta-funktsii-rimana-na-kriticheskoi-1szjr7odtc.pdf

Поведение аргумента дзета-функции Римана на критической прямой@@@Behaviour of the argument of the Riemann zeta function on the critical line

Some preliminaries some fundamental theorems on Titchmarsh series and applications Titchmarsh's phenomenon some recent progress (statements without proofs of some difficult results mentioned in the introduction). Appendix: asymptotic formulae for the gamma function and so on.

/pdf/lectures-on-on-the-mean-value-and-omega-theorems-for-the-3g668gpl9g.pdf

Lectures on on the mean-value and Omega-theorems for the Riemann zeta-function

Let $S(t)$ denote the argument of the Riemann zeta-function, defined as $$ S(t)=\dfrac{1}{\pi}\,\Im\log\zeta(1/2+it). $$ Assuming the Riemann hypothesis, we prove that $$ S(t)=\Omega_{\pm}\bigg(\dfrac{\log t\log\log\log t}{\log\log t}\bigg). $$ This improves the classical omega results of Montgomery and matches with the $\Omega$-result obtained by Bondarenko and Seip.

Large Oscillations of the Argument of the Riemann Zeta-function

/pdf/ob-argumente-dzeta-funktsii-rimana-na-kriticheskoi-priamoi-2ri15esuqc.pdf

Об аргументе дзета-функции Римана на критической прямой@@@The argument of the Riemann zeta-function on the critical line

Denote by N ( t ) the number of zeros β + iγ of ζ( s ), s = σ + it , with 0 t . It is well known that where

On the Riemann zeta-function ζ( s )—Gaps between sign changes of S ( t )

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On the Riemann zeta-function ζ( s )—Gaps between sign changes of S ( t )