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:
“The proper method of philosophy consists in clearly conceiving the insoluble problems in all their insolubility and then in simply contemplating them, fixedly and tirelessly, year after year, without any hope, patiently waiting.”
—Simone Weil (1909–1943)
“For every life and every act
Consequence of good and evil can be shown
And as in time results of many deeds are blended
So good and evil in the end become confounded.”
—T.S. (Thomas Stearns)
““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)
“I heartily wish you, in the plain home-spun style, a great number of happy new years, well employed in forming both your mind and your manners, to be useful and agreeable to yourself, your country, and your friends.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“every subjective phenomenon is essentially connected with a single point of view, and it seems inevitable that an objective, physical theory will abandon that point of view.”
—Thomas Nagel (b. 1938)