# Tagged Questions

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### Periodicity with irrational numbers [migrated]

Recently, I invented the following theorem and found a proof, it seems strange since it is very counter-intuitive to me. The proof is long and non-conceptual. Is there a place or a branch of math ...
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### Prove that the Dirichlet eta function is monotonic

Let us consider $\eta(p):= \sum\limits_{n=1}^\infty \frac{(-1)^{n+1}}{n^p}$ for $p>0$. Has anyone come along with an elementary proof that $\eta(x)$ is monotonically increasing on this set? By ...
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### Looking for a reference for a paper by Mordell

On page 384 of the book "Number Theory:Volume 1:tools and Diophantine Equations" by Henri Cohen there is reference to the fact that: "It has been proved by Schinzel, Mordell nd successors that such an ...
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### multiplicity of automorphic representation of unitary similitude group

Let $G$ be a unitary similitude group over $\mathbb{Q}$ (as in the book of Harris-Taylor), $\pi$ an irreducible automorphic representation of $G(\mathbb{A})$. I'm looking for some results on its ...
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### The number of representations of the positive integer $n$ as $a^{2}+b^{2}+p^{2}c^{2}$

Let $n$ be a positive integer and $p$ a prime number. I know that there are formulas by which one can compute the number of representations of $n$ as the sum of two or three squares etc. I would to ...
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### The maximum of the preimage of [1,x] through Euler's totient function

A friend of mine and I have shown the following: "For each $x \geq 1$ let $m := m(x)$ be the greatest positive integer such that $\varphi(m) \leq x$, where $\varphi$ is the Euler's totient function. ...
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### How to convert the formulas in definition of period numbers into their continued fraction expansion, and what will the transformation will be [closed]

As we know,there is an interpretation or correspondence of/between continued fraction expansion of numbers in/and algebraic geometry how to convert the formulas in definition of period(for reference ...
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### Optimal lower bounds for the sum of digits in base $b$

Let $b \geq 2$ be an integer and let $s_b(n)$ be the sum of the digits of the base-$b$ representation of the nonnegative integer $n$ (e.g., $s_{10}(726)=7+2+6$). From the weak law of large numbers, it ...
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