Jan Moser
Published 2010-10-05Version 1
It is proved in this paper that the Jacob's ladders together with the A. Selberg's classical formula (1942) lead to a new kind of formulae for some short trigonometric sums. These formulae cannot be obtained in the classical theory of A. Selberg, and all the less, in the theories of Balasubramanian, Heath-Brown and Ivic.
Jacob's ladders and the $\tilde{Z}^2$-transformation of a polynomials in $\ln \vp_1(t)$
Jacob's ladders and the tangent law for short parts of the Hardy-Littlewood integral
Jacob's ladders, $ΞΆ$-factorization and infinite set of metamorphosis of a multiform
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