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Category Archives: Analytic Number Theory
The Sum of the Totient Function, and Montgomery’s Lower Bound.
1 History In 1874, Mertens proved that where is Euler’s totient function. A natural question we can ask is whether or not this error term can be improved, and what we should expect it to look like. Throughout we use … Continue reading
Evaluating an infinite series in terms of the Stieltjes Constants
Motivated by this Math Stack Exchange problem the goal is to evaluate the sum for any nonnegative integer . From looking at this, it is very reasonable to expect that the answer should be a linear combination of the Stieltjes … Continue reading
Posted in Analytic Number Theory
Tagged Expansion, Laurent Series, Series, Stieltjes Constants, Zeta function
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