Problems and Results in Analytic Number Theory
The great theorems and results within analytic number theory tend not to be exact structural results about the integers, for which algebraic and geometrical tools are more appropriate. Instead, they give approximate bounds and estimates for various number theoretical functions, as the following examples illustrate.
Read more about this topic: Analytic Number Theory
Famous quotes containing the words problems, results, analytic, number and/or theory:
“All problems are finally scientific problems.”
—George Bernard Shaw (1856–1950)
“The study and knowledge of the universe would somehow be lame and defective were no practical results to follow.”
—Marcus Tullius Cicero (106–43 B.C.)
““You, that have not lived in thought but deed,
Can have the purity of a natural force,
But I, whose virtues are the definitions
Of the analytic mind, can neither close
The eye of the mind nor keep my tongue from speech.””
—William Butler Yeats (1865–1939)
“The rising power of the United States in world affairs ... requires, not a more compliant press, but a relentless barrage of facts and criticism.... Our job in this age, as I see it, is not to serve as cheerleaders for our side in the present world struggle but to help the largest possible number of people to see the realities of the changing and convulsive world in which American policy must operate.”
—James Reston (b. 1909)
“... liberal intellectuals ... tend to have a classical theory of politics, in which the state has a monopoly of power; hoping that those in positions of authority may prove to be enlightened men, wielding power justly, they are natural, if cautious, allies of the “establishment.””
—Susan Sontag (b. 1933)