# Andrew Odlyzko

Odlyzko 1986

Andrew Michael Odlyzko (born July 23, 1949 in Tarnów , Poland ) was the head of the "Mathematics of Communication and Computer Systems" department at AT&T Bell Laboratories in Murray Hill , New Jersey . He is also Professor of Mathematics at the University of Minnesota School of Mathematics . In 2001 he became the founding director of the interdisciplinary Digital Technology Center at the University of Minnesota, which he led until 2008, along with other management positions.

## Live and act

Odlyzko studied at Caltech (master's degree in 1971) and received his PhD in mathematics from the Massachusetts Institute of Technology (MIT) in Cambridge with Harold Stark ( Lower Bounds for Discriminants of Number Fields ) in 1975 . He then worked at Bell Telephone Laboratories , mainly in the areas of complexity theory , cryptography , number theory , combinatorics , coding theory , analysis and probability theory .

In 1985 he and Herman te Riele were able to refute Merten's conjecture . In the same year he and Jeffrey Lagarias and Victor S. Miller improved the Meissel - Lehmer method for calculating the number of prime numbers and calculated . Also with Lagarias, he published in 1987 an analytical method for dealing with bit complexity . Odlyzko also worked at AT&T Bell Labs (later renamed AT&T Labs) on researching the zeros of the zeta function , after working with Arnold Schönhage in 1988 on a very efficient method for the simultaneous calculation of the values ​​of the zeta function for equidistant arguments using faster Fourier transform had developed. With the help of powerful computers, he calculated up to zero points and statistically evaluated their distances. ${\ displaystyle \ pi (x)}$${\ displaystyle \ pi (10 ^ {16})}$${\ displaystyle \ pi (x)}$${\ displaystyle {\ mathcal {O}} (x ^ {{\ frac {1} {2}} + \ epsilon})}$${\ displaystyle 10 ^ {19}}$

Odlyzko was an invited speaker at the ICM 1986 in Berkeley ( New analytic algorithms in number theory ). In 2000 he received an honorary doctorate from the University of Marne-La-Vallée . He is a fellow of the American Mathematical Society .

He is the owner and co-owner of 3 patents.

His publications in the 1990s on telecommunications networks , electronic publishing , electronic commerce , the economics of data networks, etc. received attention, but some of the theses he expressed there met with contradiction. He is currently working on a book comparing the Internet euphoria to the British railroad financial bubble of the 1840s and examining implications for future technology diffusion.

As a co-author of Paul Erdős , his Erdős number is 1. He has published several works with Erdös.

3. For example P. Erdös, A. Hildebrand, A. Odlyzko, P. Pudaite, B. Reznick: The asymptotic behavior of a family of sequences, Pacific J. Math., Volume 126, 1987, pp. 227-241, P. Erdös, AM Odlyzko, A. Sarkozy: On the residues of products of prime numbers, Period. Math. Hungar., Volume 18, 1987, pp. 229-239, P. Erdös, AM Odlyzko, On the density of odd integers of the form and related questions, J. Number Theory, Volume 11, 1979, pp. 257– 263${\ displaystyle {\ frac {(p-1)} {2 ^ {k}}}}$