Related papers: An arithmetic study of the formal Laplace transfor…

We give here a new proof of a Tauberian Theorem of complex Laplace transform using the Theory of measure and theory of function with bounded variations. However we deduce the simple proof of Prime Number Theorem.

A working mathematician's summary of many results on the derived category, perverse sheaves, and vanishing cycles. This is the August 2025 version, with a completely revised section on vanishing cycles.

The functional relation coming from the $x-y$ symplectic transformation of Topological Recursion has a lot of applications, for instance it is the higher order moment-cumulant relation in free probability or can be used to compute…

This paper has been withdrawn by the corresponding author because the newest version is now published in Journal of Discrete Algorithms.

This paper has been withdrawn due to a crucial theoretical error.

In this paper, q-Laplace transforms related to the non-extensive thermodynamics are investigated by using the algebraic operation of the non-extensive calculus. The deformed simple harmonic problem is discussed by using the q-Laplace…

A Laplace transform that maps the topological recursion (TR) wavefunction to its $x$-$y$ swap dual is defined. This transform is then applied to the construction of quantum curves. General results are obtained, including a formula for the…

This paper ("Two-Level Chromophore and Irreversibility", which can be found at arXiv:0804.0086) has been withdrawn by the author due to too many errors and misleading statements. This paper has been superseded by Section 2.11 and Chapter 7…

The Laplace transform of partial sums of the square of a non-centered Gauss-Markov process, conditioning on its starting point, is explicitly computed. The parameters of multiplicative ergodicity are deduced.

We report on a formalization of the change of variables formula in integrals, in the mathlib library for Lean. Our version of this theorem is extremely general, and builds on developments in linear algebra, analysis, measure theory and…

The article has been withdrawn as its main result had already been known.

This paper has been withdrawn by the author due to a new work in [arXiv:0901.0456v4] which can contain the results in this paper.

This paper has been withdrawn. (Reason) Its contents have been entirely superseded by the contents of the articles arXiv:0809.3444 and arXiv:0705.3070. There is no profitable reason to keep it alive. No material on it is however wrong.

This paper has been withdrawn by the author because Conjecture 1 is false. Please see arXiv:0901.2093 for a justification that Conjecture 1 is false. The other main results are also available from the above URL.

This paper has been withdrawn due to a crucial theoretical and experimental error.

We deal with a real valued integral operator L of Laplace transformation type acting between Lebesgue spaces on the semi-axis. Sufficient conditions for belonging L to Schatten type classes are obtained. Some upper asymptotic estimates for…

This paper has been withdrawn due to crucial errors.

This paper has been withdrawn: it has been merged with the preprint to which it refers.

%auto-ignore The paper has been withdrawn by authors. The completely revised version can be found under the following preprint-no: hep-ph/9910282.

Submission was withdrawn by authors. arXiv:math/0305140