## Math 90: Week 11 and Midterm Solutions

We had a midterm this week, and did more review during recitation. The solutions **are now available below the fold**

We had a midterm this week, and did more review during recitation. The solutions **are now available below the fold**

Posted in Brown University, Math 90, Mathematics
Tagged Brown, Hulse, lowry, math, Math 90, mathematics, midterm, solutions, test
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In this note, I consider an application of generalized Mobius Inversion to extract information of arithmetical sums with asymptotics of the form $latex \displaystyle \sum_{nk^j \leq x} f(n) = a_1x + O(x^{1 – \epsilon})$ for a fixed $latex j$ and a constant $latex a_1$, so that the sum is over both $latex n$ and $latex k$. We will see that $latex \displaystyle \sum_{nk^j \leq x} f(n) = a_1x + O(x^{1-\epsilon}) \iff \sum_{n \leq x} f(n) = \frac{a_1x}{\zeta(j)} + O(x^{1 – \epsilon})$.

Posted in Expository, Math.NT, Mathematics
Tagged asymptotics, David Lowry, dirichlet, math, mathematics, mobius inversion, number theory, research, zeta function
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We deviated from our regular course of action this week, so we did not have preset examples to do in classes. So instead, I will say a few things, and this can be the new posthead for questions.

Posted in Brown University, Math 90, Mathematics
Tagged Brown, David Lowry, math, Math 90, mathematics
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