Jeffrey Lagarias

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Jeffrey C. Lagarias is a professor at the University of Michigan.

He was a Putnam Fellow in 1970. He received his Ph.D. in Mathematics from Massachusetts Institute of Technology in 1974. In 1975 he joined AT&T Bell Laboratories and eventually became Distinguished Member of Technical Staff. Since 1995, he has been a Technology Consultant at AT&T Research Laboratories.

While his recent work has been in theoretical computer science, his original training was in analytic algebraic number theory. He has since worked in many areas, both pure and applied, and considers himself a mathematical generalist. Among other notable accomplishments, Lagarias discovered an elementary problem that is equivalent to the Riemann Hypothesis, namely whether for all $n > 0,$ we have

$\sigma(n) \le H_n + e^{H_n} \ln{H_n}$

with equality only when $n = 1$ . Here $H n$ is the $n$ -th harmonic number, the sum of the reciprocals of the first $n$ positive integers, and $σ(n)$ is the divisor function, the sum of the positive divisors of $n$ . [1]. Lagarias has also done work on the Collatz Conjecture and Li's criterion.