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

Posted in Analytic Number Theory, Uncategorized | Tagged , , , , | 3 Comments

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 non-negative 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 , , , , | 3 Comments