Lowell Schoenfeld
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Lowell Schoenfeld
Lowell Schoenfeld
BornApril 1, 1920
DiedFebruary 6, 2002 (aged 81)
NationalityAmerican
Alma materUniversity of Pennsylvania
Scientific career
FieldsMathematics
ThesisA Transformation Formula in the Theory of Partitions (1944)
Doctoral studentsSamuel 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 ?(x) and ?(x). II", Mathematics of Computation, 30 (134): 337-360, doi:10.2307/2005976.