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Actually Ramaré's paper is freely avaible at his Lille university page (link here). The estimate that he uses to deduce his result is $$\bigg|\sum_{n\leq x} \frac{\mu(n)}{n}\bigg|\leq \bigg(\frac{3} …

It is an open problem, only known for $k=1,2$. Both the conjecture and the known cases are due to Schinzel. You can find a nice survey here: "On the third iterates of the φ- and σ-functions" H. Maie …

The answer seems to be no. It is hard to find direct confirmation, but every time their names are mentioned together it is made clear that there's no relationship. The Russian mathematician Askold …

This is for example mentioned as open in a 2010 answer by Fedor Petrov to basically a duplicate question. It might be worth noting that nothing new has been proven in these last 6 years, or it would …

Iwaniec's original proof is avaible online Henryk Iwaniec, "Almost-Primes Represented by Quadratic Polynomials" (1978) In the same paper he also proves the following lower bound for the density of …

In this paper, van der Geer and Zagier come across a concrete Hilbert cusp form of weight $6$ on $\mathrm{SL}_2(\mathcal{O})$, namely $$f=-16(x+x^{-1})^3 (q+(27x^3-39x-39x^{-1}+27x^{-3})q^2+(285x^6-7 …

As Carlo Beenakker mentions in the comments, \begin{equation*} \begin{split} -\sum_{\beta'=1/2} \mathrm{Re} \left(\frac{1}{1/2+it-\rho'}\right)&=- \mathrm{Re}\left( \frac{1}{1/2+it-(1/2+it')}\right)\ …

The answer is no. Kaczorowski and Perelli proved the classification of L-functions with degree 1, and the L-functions with that degree turn out to be the Riemann zeta function and Dirichlet L-functio …

I don't see the relation between the first sentence and the question, so perhaps I'm missing something, but the answer to the question is yes, regardless. Fourier expansion is a very important tool i …

I'm aware of Shao-Ji Feng's result that Karatsuba's weaker conjecture ("conjecture 1") is true conditionally on the Lindelöf Hypothesis. Shao-Ji Feng, "On Karatsuba conjecture and the Lindelöf hypot …

The original Pólya-Vinogradov inequality alredy works for non-primitive Dirichlet characters, $$S(\chi,x)\leq c\sqrt {q} \log q$$ for some absolute constant $c$. As J.H.S. mentions in the comments, …

A few things. All Maass forms can be written in the Bessel form that you mention. It is deduced from the growth condition of the Fourier coefficients of an arbitrary Maass forms. If you want to twis …

The only improvements seems to be $O(N^{s-1+|G/K|^{-1}}\log (N))$, avaible only in two cases: The number field is $\mathbb{Q}$ (Castillo & Dietmann, 2016) The Galois group is "small", in the sense …

It follows from the functorial properties of characters of representations (1-dimensional as in the case of Dirichlet or not) that: $$L(s,\chi) \times L(s,\psi)=L(s,\chi+\psi)$$ This basically follo …

I think there are no direct consequences of the conjecture, but it seems like the natural first step in solving the bigger orthonormality conjecture (and/or related issues like unique factorization) w …