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:
“I have a horror of people who speak about the beautiful. What is the beautiful? One must speak of problems in painting!”
—Pablo Picasso (1881–1973)
“It is perhaps the principal admirableness of the Gothic schools of architecture, that they receive the results of the labour of inferior minds; and out of fragments full of imperfection ... raise up a stately and unaccusable whole.”
—John Ruskin (1819–1900)
““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)
“States strong enough to do good are but few.
Their number would seem limited to three.”
—Robert Frost (1874–1963)
“A theory of the middle class: that it is not to be determined by its financial situation but rather by its relation to government. That is, one could shade down from an actual ruling or governing class to a class hopelessly out of relation to government, thinking of gov’t as beyond its control, of itself as wholly controlled by gov’t. Somewhere in between and in gradations is the group that has the sense that gov’t exists for it, and shapes its consciousness accordingly.”
—Lionel Trilling (1905–1975)