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Jacob's ladders and three new equivalents of the Fermat-Wiles theorem and an infinite set of these equivalents that are independent on the Jacob's ladders

Autor: Moser, Jan

In this paper we show that there is an infinite set of points of contact between the set of all Dirichlet's series and Fermat-Wiles theorem. The proof is independent on the Jacob's ladders.

Externí odkaz: http://arxiv.org/abs/2412.12692

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Jacob's ladders, almost exact decomposition of certain increments of the Hardy-Littlewood integral (1918) by means of the Raabe's integral and the thirteenth equivalent of the Fermat-Wiles theorem

Autor: Moser, Jan

In this paper we use our theory of Jacob's ladders on the Raabe's integral to obtain: (i) The thirteenth equivalent of the Fermat-Wiles theorem, as well as (ii) almost exact decomposition of certain elements of continuum set of increments of the Hard

Externí odkaz: http://arxiv.org/abs/2407.11458

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Jacob's ladders, logarithmic modification of the Hardy-Littlewood integral (1918), Titchmarsh's $\Omega$-theorem (1928) and new point of contact with the Fermat-Wiles theorem

Autor: Moser, Jan

In this paper we obtain two new points of contact between Jacob's ladders and Fermat-Wiles theorem. They are generated by a logarithmic modification of the Hardy-Littlewood integral. Furthermore, we present a kind of asymptotic laws of conservation f

Externí odkaz: http://arxiv.org/abs/2406.02278

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Jacob's ladders, Hardy-Littlewood integral (1918) and new asymptotic functional equations for Euler's Gamma function together with the tenth equivalent of the Fermat-Wiles theorem

Autor: Moser, Jan

In this paper new $\Gamma$-functional is constructed upon the basis of the set of almost linear increments of the Hardy-Littlewood integral. This functional generates a $\Gamma$-equivalent of the Fermat-Wiles theorem and also new set of factorization

Externí odkaz: http://arxiv.org/abs/2403.17522

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Jacob's ladders, almost linear increments of the Hardy-Littlewood integral (1918) and their relation to the Titchmarsh's sums (1943) and the Fermat-Wiles theorem

Autor: Moser, Jan

In this paper we give some new consequences that follow from our formula for increments of the Hardy-Littlewood integral. The main of these ones are $\mathcal{T}_1$ and $\mathcal{T}_2$ equivalents of the Fermat-Wiles theorem.
Comment: arXiv admi

Externí odkaz: http://arxiv.org/abs/2401.03781

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Jacob's ladders, almost linear increments of the Hardy-Littlewood integral (1918), the classical Dirichet's sum of divisors (1849) and their relationship with the Fermat-Wiles theorem

Autor: Moser, Jan

In this paper we obtain number of new equivalents of the Fermat-Wiles theorem that are based on Jacob's ladders. The main of these is the $D$-equivalent that is generated by the Dirichlet's $D(x)$-function.

Externí odkaz: http://arxiv.org/abs/2312.12085

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Jacob's ladders, almost linear increments of the Hardy-Littlewood integral (1918) and their relations to the Selberg's formula (1946) and the Fermat-Wiles theorem

Autor: Moser, Jan

In this paper we give new consequences that follow from our formula for increments of the Hardy-Littlewood integral. Main of these consequences is an $\zeta$-equivalent of the Fermat-Wiles theorem. It is expressed purely by means of the Riemann's zet

Externí odkaz: http://arxiv.org/abs/2306.07648

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Jacob's ladders, existence of almost linear increments of the Hardy-Littlewood integral and new types of multiplicative laws

Autor: Moser, Jan

In this paper we prove that there is a continuum set of increments with some minimal structure for the Hardy - Littlewood integral. The result implies a number of new properties of the Hardy - Littlewood integral.

Externí odkaz: http://arxiv.org/abs/2304.09267

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Jacob's ladders and vector operator producing new generations of $L_2$-orthogonal systems connected with the Riemann's $\zeta(\frac 12+it)$ function

Autor: Moser, Jan

In this paper we introduce a generating vector-operator acting on the class of functions $L_2([a,a+2l])$. This operator produces (for arbitrarily fixed $[a,a+2l]$) infinite number of new generation $L_2$-systems. Every element of the mentioned system

Externí odkaz: http://arxiv.org/abs/2302.07508

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Jacob's ladders, class of crossbreeding conserving certain cell of meta-functional equations and existence of cancerous growth of that cell

Autor: Moser, Jan

In this paper a set of 48 crossbreedings on certain cell of meta-functional equations preserving the cell is obtained. In opposite direction we presente an example of very complicated meta-functional equation not obtained in basic cell though it is g

Externí odkaz: http://arxiv.org/abs/2105.07780

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