![Number Theory (trends In Mathematics)](/media/uploads/2018/5/number-theory-trends-in-mathematics.jpg)
Number Theory (trends In Mathematics)
by R.P. Bambah /
2000 / English / DjVu
10.5 MB Download
The Indian National Science Academy on the occasion ofthe Golden
Jubilee Celebration (Fifty years of India's Independence) decided
to publish a number of monographs on the selected fields. The
editorial board of INS A invited us to prepare a special monograph
in Number Theory. In reponse to this assignment, we invited several
eminent Number Theorists to contribute expository/research articles
for this monograph on Number Theory. Al though some ofthose
invited, due to other preoccupations-could not respond positively
to our invitation, we did receive fairly encouraging response from
many eminent and creative number theorists throughout the world.
These articles are presented herewith in a logical order. We are
grateful to all those mathematicians who have sent us their
articles. We hope that this monograph will have a significant
impact on further development in this subject. R. P. Bambah v. C.
Dumir R. J. Hans-Gill A Centennial History of the Prime Number
Theorem Tom M. Apostol The Prime Number Theorem Among the thousands
of discoveries made by mathematicians over the centuries, some
stand out as significant landmarks. One of these is the prime
number theorem, which describes the asymptotic distribution of
prime numbers. It can be stated in various equivalent forms, two of
which are: x (I) K(X) '" -I - as x --+ 00, ogx and Pn '" n log n as
n --+ 00. (2) In (1), K(X) denotes the number of primes P ::s x for
any x > O.
The Indian National Science Academy on the occasion ofthe Golden
Jubilee Celebration (Fifty years of India's Independence) decided
to publish a number of monographs on the selected fields. The
editorial board of INS A invited us to prepare a special monograph
in Number Theory. In reponse to this assignment, we invited several
eminent Number Theorists to contribute expository/research articles
for this monograph on Number Theory. Al though some ofthose
invited, due to other preoccupations-could not respond positively
to our invitation, we did receive fairly encouraging response from
many eminent and creative number theorists throughout the world.
These articles are presented herewith in a logical order. We are
grateful to all those mathematicians who have sent us their
articles. We hope that this monograph will have a significant
impact on further development in this subject. R. P. Bambah v. C.
Dumir R. J. Hans-Gill A Centennial History of the Prime Number
Theorem Tom M. Apostol The Prime Number Theorem Among the thousands
of discoveries made by mathematicians over the centuries, some
stand out as significant landmarks. One of these is the prime
number theorem, which describes the asymptotic distribution of
prime numbers. It can be stated in various equivalent forms, two of
which are: x (I) K(X) '" -I - as x --+ 00, ogx and Pn '" n log n as
n --+ 00. (2) In (1), K(X) denotes the number of primes P ::s x for
any x > O.