The Journal of the Indian Mathematical Society

Paul Turan

Abstract

The investigations of this paper refer to that trend in the theory of diophantine approximation whose necessity I realised some years ago and whose fertility turned out in its applicability to different branches of analysis and number theory ever since.

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Paul Turan ¹

Affiliations
1 University of Budapest, HU

Abstract

More than a hundred years have passed since Riemann published his fundamental work on prime numbers. Many investigations have been published to prove its audacious unproved assertions, and still more to make clear the various questions about the distribution of the zeros which were raised mainly by number theory. These questions and investigations are contained, by and large, in the following five groups.

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Paul Turan ¹

Affiliations
1 Budapest, HU

Abstract

The classical conjecture of Fermat, unpoved so far, asserts that the equation

x^q + y^q = z^q (I, I)

is unsolvable in positive integers if q is a fixed integer ≥ 3. The history of the (few) attempts, which mean a progress however slight in this direction, is well known.

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