| In 1829, Dirichlet deduced the representability by Fourier series of a class of functions defined by concepts. |
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| This work led him to the Dirichlet problem concerning harmonic functions with given boundary conditions. |
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| He attended courses by Dirichlet on the theory of numbers, on potential theory, on definite integrals, and on partial differential equations. |
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| Beurling worked on the theory of generalized functions, differential equations, harmonic analysis, Dirichlet series and potential theory. |
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| Among Dedekind's other notable contributions to mathematics were his editions of the collected works of Peter Dirichlet, Carl Gauss, and Georg Riemann. |
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| A theorem of Peter Gustav Lejeune Dirichlet on primes in arithmetic progression guarantees that all the other notes are heard infinitely often when one plays all the primes. |
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| For parabolic equations and for the exterior Dirichlet problem, it is possible to apply the well known mean value theorems. |
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| Keywords Smarandache LCM dual function, Dirichlet series, exact calculating formula, asymptotic formula. |
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| This requires the associated multiplicative function, say f, to have special enough properties that the associated Dirichlet series may be analytically continued. |
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| Keywords Continued fractions, Dirichlet L-functions, identities. |
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