How Long to Read Capacity Theory on Algebraic Curves

How Long Does it Take to Read Capacity Theory on Algebraic Curves?

It takes the average reader 7 hours and 22 minutes to read Capacity Theory on Algebraic Curves by Robert S. Rumely

Assuming a reading speed of 250 words per minute. Learn more

Description

Capacity is a measure of size for sets, with diverse applications in potential theory, probability and number theory. This book lays foundations for a theory of capacity for adelic sets on algebraic curves. Its main result is an arithmetic one, a generalization of a theorem of Fekete and Szegö which gives a sharp existence/finiteness criterion for algebraic points whose conjugates lie near a specified set on a curve. The book brings out a deep connection between the classical Green's functions of analysis and Néron's local height pairings; it also points to an interpretation of capacity as a kind of intersection index in the framework of Arakelov Theory. It is a research monograph and will primarily be of interest to number theorists and algebraic geometers; because of applications of the theory, it may also be of interest to logicians. The theory presented generalizes one due to David Cantor for the projective line. As with most adelic theories, it has a local and a global part. Let /K be a smooth, complete curve over a global field; let Kv denote the algebraic closure of any completion of K. The book first develops capacity theory over local fields, defining analogues of the classical logarithmic capacity and Green's functions for sets in (Kv). It then develops a global theory, defining the capacity of a galois-stable set in (Kv) relative to an effictive global algebraic divisor. The main technical result is the construction of global algebraic functions whose logarithms closely approximate Green's functions at all places of K. These functions are used in proving the generalized Fekete-Szegö theorem; because of their mapping properties, they may be expected to have other applications as well.

How long is Capacity Theory on Algebraic Curves?

Capacity Theory on Algebraic Curves by Robert S. Rumely is 441 pages long, and a total of 110,691 words.

This makes it 149% the length of the average book. It also has 135% more words than the average book.

How Long Does it Take to Read Capacity Theory on Algebraic Curves Aloud?

The average oral reading speed is 183 words per minute. This means it takes 10 hours and 4 minutes to read Capacity Theory on Algebraic Curves aloud.

What Reading Level is Capacity Theory on Algebraic Curves?

Capacity Theory on Algebraic Curves is suitable for students ages 12 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Capacity Theory on Algebraic Curves?

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