Preprint Hypothesis Version 1 Preserved in Portico This version is not peer-reviewed

# A Direct Approach for the Lindelöf Conjecture Related to Theory of the Riemann Zeta Function

Version 1 : Received: 26 April 2021 / Approved: 27 April 2021 / Online: 27 April 2021 (09:46:32 CEST)

How to cite: Yang, X. A Direct Approach for the Lindelöf Conjecture Related to Theory of the Riemann Zeta Function. Preprints 2021, 2021040698 (doi: 10.20944/preprints202104.0698.v1). Yang, X. A Direct Approach for the Lindelöf Conjecture Related to Theory of the Riemann Zeta Function. Preprints 2021, 2021040698 (doi: 10.20944/preprints202104.0698.v1).

## Abstract

It is due to Littlewood that the truth of the Riemann theorem implies that of the Lindel\"{o}f conjecture. This paper aims to use the idea of Littlewood to prove the Lindel\"{o}f conjecture for the Riemann zeta function. The Lindel\"{o}f $\mu$ function at the critical line is zero, with use of the Riemann theorem for the entire Riemann zeta function, proved based on the work of Heath-Brown. Our result is given to show that the Lindel\"{o}f conjecture, connected with the proof of the moment conjecture, is true.

## Subject Areas

Lindelöf conjecture; Riemann zeta function; nontrivial zeros; Riemann theorem; moment conjecture

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