Lowell Schoenfeld

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:

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

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

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, JSTOR 2005976.

External links

• Lowell Schoenfeld at the Mathematics Genealogy Project