A Walker

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bio website integermiscellany.wordpress.c… location Providence, RI age 24 member for 3 years, 6 months seen Dec 8 at 23:49 profile views 421

I am a third-year graduate student of mathematics at Brown University, working under the direction of Jeff Hoffstein. My interests touch upon a variety of topics in analytic number theory.

I maintain a mathematics blog, integer miscellany, through which I present some of my shorter mathematical work.

 76 Proof that ${\left(\pi^\pi\right)}^{\pi^\pi}$ (and now $\pi^{\left(\pi^{\pi^\pi}\right)}$) is a noninteger 47 What is the role of mathematical intuition and common sense in questions of irrationality or transcendence of values of special functions? 22 Cool mathematics I can show to calculus students. 12 Conjectural closed-form representations of sums, products or integrals 7 Find what values of $n$ give $\varphi(n) = 10$

4,564 Reputation

 +5 Asymptotics of a Cauchy Product +10 Prime counting inequality +50 Proof that ${\left(\pi^\pi\right)}^{\pi^\pi}$ (and now $\pi^{\left(\pi^{\pi^\pi}\right)}$) is a noninteger +5 Numbers which are “Provably Difficult to Compute”?

26 Questions

 14 Necessary and sufficient conditions for a polynomial in $\mathbb{Z}[t]$ to have an $n$th root in $\mathbb{Z}[[t]]$ 10 Is there an intuitive proof of the identity $\sum_{L \subset S} \prod_{x \in L} (x-1) = \prod_{x \in S} x$ from general principles? 9 Prove that $\sum_{n=1}^\infty \mu(n) \log n/n =1$. 8 A field which is not algebraically closed but has no extensions of a fixed degree(s)? 8 Prove that a holonomic (p-recursive) difference equation returns only integral values

98 Tags

 118 number-theory × 24 47 irrational-numbers 82 numerical-methods × 2 47 philosophy 78 arithmetic × 2 47 special-functions 55 gamma-function × 4 26 sequences-and-series × 11 47 transcendental-numbers × 2 21 elementary-number-theory × 9

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 Mathematics 4,564 rep 1127