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:
“While the onset of puberty can vary by as much as six years, every adolescent wants to be right on the 50-yard line, right in the middle of the field. One is always too tall, too short, too thin, too fat, too hairy, too clear-skinned, too early, too late. Understandably, problems of self-image are rampant.”
—Joan Lipsitz (20th century)
“The chief benefit, which results from philosophy, arises in an indirect manner, and proceeds more from its secret, insensible influence, than from its immediate application.”
—David Hume (1711–1776)
““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 am walking over hot coals suspended over a deep pit at the bottom of which are a large number of vipers baring their fangs.”
—John Major (b. 1943)
“Don’t confuse hypothesis and theory. The former is a possible explanation; the latter, the correct one. The establishment of theory is the very purpose of science.”
—Martin H. Fischer (1879–1962)