<em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

    <em id="zlul0"></em>

      <dl id="zlul0"></dl>
        <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
        <em id="zlul0"></em>

        <div id="zlul0"><ol id="zlul0"></ol></div>

        Stack Exchange Network

        Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

        Visit Stack Exchange

        Questions tagged [analytic-number-theory]

        A beautiful blending of real/complex analysis with number theory. The study involves distribution of prime numbers and other problems and helps giving asymptotic estimates to these.

        3
        votes
        0answers
        23 views

        What is meant by singular hyperplane of $c(w, \cdot)$? (global intertwining operator related to Eisenstein series)

        Let $P_0$ be a minimal $\mathbb{Q}$-parabolic subgroup of $G$, a semisimple linear algebraic group over $\mathbb{Q}$. Then $P_0 = M_0 N_0$ where $M_0$ is a Levi subgroup of $P_0$. Let $E^G_{P_0}$ be ...
        1
        vote
        0answers
        75 views

        Primes with given Hamming weight

        If I understand correctly, in the following MO-thread Are There Primes of Every Hamming Weight? two users of the site claim that it has been already proven that, for every sufficiently large $n \in \...
        4
        votes
        2answers
        460 views

        Estimate related to the Möbius function

        I need to know, or at least have a good bound for, the asymptotic behaviour on $x$ of amount of integers less or equal than $x$ that are square free and with exactly $k$ primes on its decomposition. ...
        1
        vote
        0answers
        187 views

        An implication of the Zagier et al result on the hyperbolicity of Jensen polynomials for the Riemann zeta function?

        In their paper recently published in the PNAS, Zagier et al demonstrated that The Jensen polynomials $J_{\alpha}^{d,n}(X)$ of the Riemann zeta function of degree $d$ and shift $n$ are hyperbolic for ...
        4
        votes
        3answers
        304 views

        Positive proportion of logarithmic gaps between consecutive primes

        For $x, \lambda > 0$, define $$S_\lambda(x) := \#\{p_{n+1} \leq x : p_{n+1} - p_n \geq \lambda \log x\} ,$$ where $p_n$ is the $n$th prime number. It is known [1] that an uniform version of the ...
        7
        votes
        0answers
        164 views

        Primes $p\in(n,2n)$ with $(\frac{-n}p)=-1$

        Bertrand's postulate proved by Chebyshev states that for any $x>1$ there is a prime $p$ in the interval $(x,2x)$. In 2012 I considered some refinements of this by imposing additional requirement ...
        4
        votes
        0answers
        256 views

        Question on an application of Langlands' result on the constant term of Eisenstein series (Is this a typo?)

        I would like to understand an argument in https://link.springer.com/content/pdf/10.1007/BF01393904.pdf, which uses Langlands' result on the constant term of Eisenstein series, but I'm not getting it ...
        13
        votes
        1answer
        519 views

        Why do Maynard-Tao weights succeed?

        I'm attempting to understand why the Maynard-Tao weights are successful in proving bounded gaps between primes, but the GPY weights are not. These two posts do an excellent job in giving an overview ...
        2
        votes
        1answer
        99 views

        The minimal volume of the intersection of two $\mathscr{l}_1$-ball in high dimension

        We define $$B_1(r,c) = \{x\in\mathbb{R}^d : \Vert{}x-c\Vert_1 \le r\}$$ Now for arbitrary constant $r \ge s > 0$, given constant $\epsilon \in (r-s,r+s)$, considering $v \in \mathbb{R}^d$ such ...
        6
        votes
        1answer
        263 views

        Rate of convergence of the prime zeta function P(2)

        For an application in statistical group theory, we need explicit upper and lower bounds that an expert in number theory (I am not one) may know how to prove. Question 1: What are "good" bounds $f_1(x)...
        2
        votes
        1answer
        276 views

        Conditional bound on RH for $\Re\left(\sum_{p\leq\sqrt{x}}\frac{(1/2)}{p^{1+2it}}\right)$

        I would like to prove that Assume RH. Let $T$ large, $2\leq x \leq T^2$ and $T\leq t \leq 2T$, then $$ \log|\zeta(1/2+it))|\leq \Re\left(\sum_{p\leq x}\frac{1}{p^{1/2+1/\log x+it}}\frac{\log(x/p)}...
        0
        votes
        0answers
        60 views

        General Term Formula for Sequences

        Let $k_1,k_2,\cdots,k_n,\cdots$ be a sequence of known positive numbers. Define $$ a_1:=k_1,\\ a_2:=C_2^2k_2+C_2^1k_1a_1,\\ a_3:=C_3^3k_3+C_3^2k_2a_1+C_3^1k_1a_2,\\ a_4:=C_4^4k_4+C_4^3k_3a_1+C_4^...
        1
        vote
        1answer
        117 views

        Complex integral of logarithmic derivative of $\zeta$

        I want to prove that for any $x\geq 2$ we have $$ \begin{split} -\frac{\zeta^{\prime}}{\zeta}(s)&=\sum_{n\leq x}\frac{\Lambda(n)}{n^s}\frac{\log(x/n)}{\log x}+\frac{1}{\log x}\left(\frac{\zeta^{\...
        2
        votes
        0answers
        158 views

        Trying to understand why Eisenstein series is well defined

        I am struggling to see why Eisenstein series is well defined, and I would greatly appreciate clarification. Let $$ E(x, \lambda) = \sum_{\delta \in P(\mathbb{Q}) \backslash G(\mathbb{Q}) } e^{\...
        1
        vote
        1answer
        112 views

        Upper bound of signed exponential sums

        I am wondering whether I can get the upper bound in closed form of $$\sum_{n=1}^N(\alpha \exp(j2\pi n/N)) \text{ where } \alpha = +1\text{ or }-1 \text{ and } j^2=-1.$$ If alpha is just positive one,...

        15 30 50 per page
        山西福彩快乐十分钟
          <em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

          <em id="zlul0"></em>

            <dl id="zlul0"></dl>
              <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
              <em id="zlul0"></em>

              <div id="zlul0"><ol id="zlul0"></ol></div>
                <em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

                <em id="zlul0"></em>

                  <dl id="zlul0"></dl>
                    <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
                    <em id="zlul0"></em>

                    <div id="zlul0"><ol id="zlul0"></ol></div>
                    梦幻诛仙破解版 好运经纪人闯关 属狗的幸运生肖是什么 沃尔夫斯堡vs奥格斯堡 牛仔和外星人百度影音 上海快三走势图基本图 猎鱼达人3d 比基尼派对电影 达祖部落拉措 快乐假日游戏