# Lowell Schoenfeld

Lowell Schoenfeld
Born April 1, 1920
Died February 6, 2002 (aged 81)
Nationality  United States
Alma mater University of Pennsylvania
Scientific career
Fields Mathematics
Thesis A Transformation Formula in the Theory of Partitions (1944)
Doctoral students Samuel Lawn

Lowell Schoenfeld (April 1, 1920 – February 6, 2002) was an American mathematician known for his work in analytic number theory. He received his Ph.D. in 1944 from University of Pennsylvania under the direction of Hans Rademacher. He is known for obtaining the following results in 1976, assuming the Riemann hypothesis:

${\displaystyle |\pi (x)-{\rm {li}}(x)|\leq {\frac {{\sqrt {x}}\,\ln x}{8\pi }}}$

for all x ≥ 2657, based on the prime-counting function π(x) and the logarithmic integral function li(x), and

${\displaystyle |\psi (x)-x|\leq {\frac {{\sqrt {x}}\,\ln ^{2}x}{8\pi }}}$

for all x ≥ 73.2, based on the second Chebyshev function ψ(x).[1]

## References

1. ^ ——— (1976), "Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x). II", Mathematics of Computation, 30 (134): 337–360, doi:10.2307/2005976.