<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 [algebraic-number-theory]

        Algebraic number fields, Algebraic integers, Arithmetic Geometry, Elliptic Curves, Function fields, Local fields, Arithmetic groups, Automorphic forms, zeta functions, $L$-functions, Quadratic forms, Quaternion algebras, Homogenous forms, Class groups, Units, Galois theory, Group cohomology, Étale cohomology, Motives, Class field theory, Iwasawa theory, Modular curves, Shimura varieties, Jacobian varieties, Moduli spaces

        2
        votes
        1answer
        59 views

        Norms of elements in a quadratic order - can you do it elementarily?

        Let $\mathcal O$ be an order in an imaginary quadratic field $K$. Does there exists an element $\lambda\in \mathcal O$ such that the norm $N(\lambda)$ is not a square? Does there exists an element $\...
        4
        votes
        1answer
        124 views

        Discriminant of a radical extension of a quadratic number field

        Let $K=\mathbb Q(\sqrt 5)$ and $\varepsilon = \frac{3 + \sqrt 5}{2}$ its totally positive fundamental unit (i.e. it generates the subgroup of totally positive units). For any $n \geq 3$, let $L_n = K(\...
        0
        votes
        0answers
        132 views

        ask for reference on Grothendieck trace formula

        recently I need to refer to the so called Grothendieck trace formula, but after scanned tens of Google pages, I still can not find a proper reference on that topic, could anyone told me some good book/...
        0
        votes
        1answer
        104 views

        On exponential polynomials

        Suppose we have the following function $f:\mathbb{R}^{+}\mapsto \mathbb{R}$ $$f(t)=\sum_{i=1}^k P_i(t)\exp(\alpha_i t),$$ where $\alpha_i$s are all algebraic numbers and $P_i(t)$ are all polynomials ...
        2
        votes
        0answers
        112 views

        Number of degree d curves passing through d points in the projective plane over a finite field

        Let the base field be a finite field $\mathbb F_q$ and fix $d$ rational points that lie on a line in $\mathbb P^2$. Suppose $d$ is a large number (about the order of $q^{\alpha}$ for $\alpha$ some ...
        1
        vote
        0answers
        82 views

        Hilbert modular form as a representation of Hecke algebra

        I am reading some notes by Snowden and I don't understand a sentence. Clearly, if we have an appropriate $R = T$ theorem then we get a modularity lifting theorem, as $\rho$ defines a homomorphism ...
        4
        votes
        1answer
        193 views

        Estimation of a sum of algebraic numbers

        Let $\alpha_1, \ldots, \alpha_n$ be algebraic numbers and let $p_1, \ldots, p_n$ be the corresponding minimal polynomials with integer coefficients. Denote by $H$ the maximal magnituge among all ...
        2
        votes
        0answers
        110 views

        Ramification concept in complex analysis and algebraic number theory

        I have a question about the connection between the concept of ramification/branching out for Riemann surfaces and algebraic number theory: In the theory of Riemann surfaces we have following ...
        1
        vote
        0answers
        66 views

        Proper ideals are invertible

        I am reading through Cox's book Primes of the form $x^2+ny^2$ and I am stuck with some proofs in Chapter 7 (I have the 2nd edition). There, the author presents the following Lemma: Lemma 7.5: Let $...
        5
        votes
        1answer
        117 views

        What are the modularity properties of Weierstrass sigma function?

        I'm a little confused at the sigma orientation of tmf, see e.g. Witten genus and its references. The Weierstrass sigma function can be written as $$\sigma_L(z)(q)=\frac{z}{\exp\left(\sum_{k\ge 2} G_k(...
        1
        vote
        1answer
        99 views

        How to find a cyclotomic polynomial of degree d that decompose into d irreducible polynomials in $Z_6$?

        More specifically, I need the degree $d$ to be around 1024. I can easily find the cyclotomic polynomial of degree 1024 that satisfies the above requirement in $Z_2$, i.e., $x^{1024}+1$, which is equal ...
        11
        votes
        2answers
        815 views

        History of the Frobenius Endomorphism?

        The existence of the Frobenius endomorphism probably goes back to Euler's proof of Fermat's little theorem. But why is it named after Frobenius? Who gave it this name? When was it first stated in full ...
        2
        votes
        0answers
        102 views

        What is the definition of ''geometrically irreducible closed curve''?

        In the algebraice geometry, one says about "geometrically irreducible closed curve" over field $k$. For example, the theorem 5.4.5 (pp. 147) of ''Heights in Diophantine Geometry'' of E. Bombieri wrote ...
        4
        votes
        0answers
        45 views

        Average minimal index of cyclic cubic fields

        It is known that the set of binary cubic forms $$\displaystyle T_3 = \{F_{a,b}(x,y) = ax^3 + bx^2 y + (b - 3a)xy^2 - ay^3 : a,b \in \mathbb{Z}\}$$ parametrize the set of cyclic cubic fields, in the ...
        2
        votes
        0answers
        157 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^{\...

        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>
                    pk10 尤文图斯欧冠马竞8分之一 福彩欢乐生肖怎么玩 泰国天堂电子游艺 堡垒之夜英文 mg东方珍兽怎么刷水 法甲蒙彼利埃对甘冈预测比分 迪拜法兰克福汽配展 波斯波利斯宫遗址怎么样 王者传说皮肤