Read e-book online Advances in number theory: Proc. 3rd conf. of Canadian PDF

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By Fernando Q. Gouvea, Noriko Yui

ISBN-10: 0198536682

ISBN-13: 9780198536680

This ebook includes the court cases of the 3rd convention of the Canadian quantity thought organization. The 38 technical papers provided during this quantity speak about suitable and well timed concerns within the fields of analytic quantity concept, arithmetical algebraic geometry, and diophantine approximation. The booklet comprises numerous papers honoring Paulo Ribenboim, to whom this convention used to be devoted.

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Additional info for Advances in number theory: Proc. 3rd conf. of Canadian Number Theory Association, 1991

Example text

But Riemann's zeta function behaves in a very different way, fluctuating wildly and even sometimes equalling zero for some values of s. Those values of s that make Riemann's zeta function zero hold the secret of how the primes are distributed. That's because 5 in the Riemann zeta function is a different type of number altogether from the 5 in Euler's zeta function. Riemann used numbers which mathematicians call 'imaginary numbers: And that's a whole new story. o New numbers for old The imaginary number is a fine and wonderful recourse of the divine spirit, almost an amphibian between being and not being.

It so happens that mathematicians have created a type of number that is not to be found on the street of real numbers. These numbers, called complex numbers, spread out on either side of that street, into the unurbanized landscape that we have so 31 - New numbers for old • 43 far thought of as bare and uninteresting. Without yet worrying about how or why the mathematicians have done this, let's just say that these numbers run along streets that are at right angles to the main street of real numbers.

The i is a useful marker which enables us to identify the part of the complex number that is on an axis at right angles to the real number axis. But it turns out to have a much more useful function in certain types of equations: i is a number which can be taken to represent the concept 'the square root of -1'. It's rare that literature deals with mathematics in an informed way. But there's a conversation in the novel Young Tor/ess, by the German writer Robert Musil, that illustrates the puzzling nature of i.

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Advances in number theory: Proc. 3rd conf. of Canadian Number Theory Association, 1991 by Fernando Q. Gouvea, Noriko Yui


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