Some Applications of Laplace Transforms in Analytic Number Theory
نویسنده
چکیده
Integral transforms play an important rôle in Analytic number theory, the part of Number theory where problems of a number-theoretic nature are solved by the use of various methods from Analysis. The most common integral transforms that are used are: Mellin transforms (Robert Hjalmar Mellin, 18541933), Laplace transforms (Pierre-Simon, marquis de Laplace, 1749-1827) and Fourier transforms (Joseph Fourier, 1768-1830). Crudely speaking, suppose that one has an integral transform
منابع مشابه
L2-transforms for boundary value problems
In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.
متن کاملAxisymmetric Problem of Thick Circular Plate with Heat Sources in Modified Couple Stress Theory
The main aim is to study the two dimensional axisymmetric problem of thick circular plate in modified couple stress theory with heat and mass diffusive sources. The thermoelastic theories with mass diffusion developed by Sherief et al. [1] and kumar and Kansal [2] have been used to investigate the problem. Laplace and Hankel transforms technique is applied to obtain the solutions of the governi...
متن کاملA Century of Complex Tauberian Theory
Complex-analytic and related boundary properties of transforms give information on the behavior of pre-images. The transforms may be power series, Dirichlet series or Laplace-type integrals; the pre-images are series (of numbers) or functions. The chief impulse for complex Tauberian theory came from number theory. The first part of the survey emphasizes methods which permit simple derivations o...
متن کاملDensities, Laplace Transforms and Analytic Number Theory
Li showed that the Riemann Hypothesis is equivalent to the nonnegativity of a certain sequence of numbers. Bombieri and Lagarias gave an arithmetic formula for the number sequence based on the Guinand-Weil explicit formula and showed that Li's criterion is equivalent to Weil's criterion for the Riemann Hypothesis. We provide a derivation of the explicit formula based on Laplace transforms and p...
متن کاملIn nitely divisible laws associated with hyperbolic functions
The in nitely divisible distributions on R+ of random variables Ct, St and Tt with Laplace transforms 1 cosh p 2 t ; p 2 sinh p 2 !t ; and tanh p 2 p 2 !t respectively are characterized for various t > 0 in a number of di erent ways: by simple relations between their moments and cumulants, by corresponding relations between the distributions and their L evy measures, by recursions for their Mel...
متن کامل