Jacob's ladders and the asymptotic formula for short and microscopic parts of the Hardy-Littlewood integral of the function $|\zeta(1/2+it)|^4$
Abstract
The elementary geometric properties of Jacob's ladders of the second order lead to a class of new asymptotic formulae for short and microscopic parts of the Hardy-Littlewood integral of $|\zeta(1/2+it)|^4$. These formulae cannot be obtained by methods of Balasubramanian, Heath-Brown and Ivic.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2010
- DOI:
- 10.48550/arXiv.1001.4007
- arXiv:
- arXiv:1001.4007
- Bibcode:
- 2010arXiv1001.4007M
- Keywords:
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- Mathematics - Classical Analysis and ODEs