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If you consult Lehmer's paper, the terms in question arise from $$P_2(x, a) = \sum_{p_a < p_i \le \frac x{p_i}} \sum_{p_i \le p_j \le \frac x{p_i}} 1 = \sum_{p_a < p_i \le b} \left\{ \pi\left(\frac x{ …

I was looking for the same claim about another mathematician (namely Vazgain Avanissian) that I came to this question. Following the clues left by the previous answer and the comments, I found a menti …

Related to Which complete orthomodular lattices arise from von Neumann algebras? but I post only one answer here. A improved version of the question is: extend von Neumann equivalence for finite facto …

Let me first clarify some confusion in the comments to the original question. To be clear : I'm not at all saying the persons making them were confused, as far as I can tell all the comments were corr …

Yes, such domain exists. Let $P$ be Poincare homology 3-sphere. And $X= P\times I - D^3\times I$, then $X$ can be smoothly embedded in $S^4$(mostly the double of $X$ is $S^4$) . Let $\Omega$ be a smal …

For $h:=\Delta t>0$, you had $$P(\tau>t)-P(\tau>t+h)=\int_{(0,\infty)} P(M\le-x|X_t=x)\,P(X_t\in dx),$$ where $$M:=\inf_{t\le u\le t+h}J_u,\quad J_u:=\int_t^u a(s,X_s)\,dW_s.$$ By Doob's martingale in …

Consider two diffusions given by $$X_j(t)=\int_0^t a_j(s,X_j(s))\,dW_s$$ for $j=1,2$ and $t\ge 0$, where $W_\cdot$ is a standard Wiener process/Brownian motion and the $a_j$'s are smooth enough functi …

I am looking to find real quadratic fields whose Hilbert class field is abelian over $\Bbb Q$. Then I learned about genus numbers and genus field of the number field. It is enough to find a number fie …

This is a question about whether or not some number $\lambda^*$ is normal in base 2. More specifically, I am wondering if $\lambda^*$ is not normal. Proving it is normal would be next to impossible, a …

Many famous number-theorists have written about the history of the theory of numbers. One of the most prominent examples is that of André Weil (1906-1998): not only did he author epoch-making papers i …

Edit 2/15/2022{ The utility of the Gaussian $e^{\frac{t^2}{2}}$--its numerous properties--derives from the nature of the coefficients of its Taylor series expansion, naturally. The coefficients, which …

Context: In this and this paper, J. Arias de Reyna shows that the RH follows when: $$1.2663935... \le \sum_{n=1}^\infty A_n^2 \le 1.2723669...$$ where $A_n$ is the coefficient in the following power …

I am reading this paper by Csiszar. Given a probability measure $R$ and a convex subset $\mathcal{E}$ of probability distributions, it defines ‘I-projection of R on $\mathcal{E}$’ (provided there exis …

I'm currently reading the paper Well-posedness for the Zakharov system with the periodic boundary condition by Takaoka. In the proof of Lemma 2.3 about the integral $I_1$ one needs to establish the es …

The question asks what is known about integer solutions $(\mathbf{x}, \mathbf{y}) = ((x_1, x_2, x_3), (y_1, y_2, y_3))$ to the equation $$\displaystyle x_1^{r-1} y_1^r + x_2^{r-1} y_2^r = x_3^{r-1} y_ …