His family hailed from the town of Richelet in Belgium, from which his surname "Lejeune Dirichlet" ("le jeune de Richelet" = "the young chap from Richelet") was derived, and that was where his grandfather lived.
Dirichlet was born in Düren, where his father was the postmaster. He was educated in Germany, and then France, where he learnt from many of the most renowned mathematicians of the day. His first paper was on Fermat's Last Theorem. This was a famous conjecture (now proven) that stated that for n > 2, the equation xn + yn = zn has no solutions, apart from the trivial ones in which x, y, or z is zero. He produced a partial proof for the case n = 5, which was completed by Adrien-Marie Legendre, who was one of the referees. Dirichlet also completed his own proof almost at the same time; he later also produced a full proof for the case n = 14.
He married Rebecca Mendelssohn, who came from a distinguished Jewish family, being a granddaughter of the philosopher Moses Mendelssohn, and a sister of the composer Felix Mendelssohn.
After his death, Dirichlet's lectures and other results in number theory were collected, edited and published by his friend and fellow mathematician Richard Dedekind under the title Vorlesungen über Zahlentheorie (Lectures on Number Theory).
"Johann Peter Gustav Lejeune Dirichlet (http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Dirichlet.html)", MacTutor History of Mathematics, University of St Andrews.
Dirichlet, Johann Peter Gustav Lejeune, Vorlesungen uber Zahlentheorie. Braunschweig, 1863. "Number Theory for the Millennium (http://www.scs.uiuc.edu/~mainzv/exhibitmath/bkgd/dirichlet-bkgd.htm)".
His family hailed from the town of Richelet in Belgium, from which his surname "Lejeune Dirichlet" ("le jeune de Richelet" = "the young chap from Richelet") was derived, and that was where his grandfather lived.
Dirichlet was born in Düren, where his father was the postmaster.
After his death, Dirichlet's lectures and other results in number theory were collected, edited and published by his friend and fellow mathematician Richard Dedekind under the title Vorlesungen über Zahlentheorie (Lectures on Number Theory).
In general the abscissa of convergence of a Dirichlet series is the intercept on the real axis of the vertical line in the complex line, such that there is convergence to the right of it, and divergence to the left.
This is the analogue for Dirichlet series of the radius of convergence for power series.
The Dirichlet series case is more complicated, though: absolute convergence and uniform convergence may occur in distinct half-planes.
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