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Displaying 2121 – 2140 of 3028

On the higher power moments of cusp form coefficients over sums of two squares

Guodong Hua (2022)

Czechoslovak Mathematical Journal

Let $f$ be a normalized primitive holomorphic cusp form of even integral weight for the full modular group $Γ = SL (2, ℤ)$ . Denote by $λ_{f} (n)$ the $n$ th normalized Fourier coefficient of $f$ . We are interested in the average behaviour of the sum $\sum_{a^{2} + b^{2} \leq x} λ_{f}^{j} (a^{2} + b^{2})$ for $x \geq 1$ , where $a, b \in ℤ$ and $j \geq 9$ is any fixed positive integer. In a similar manner, we also establish analogous results for the normalized coefficients of Dirichlet expansions of associated symmetric power $L$ -functions and Rankin-Selberg $L$ -functions.

On the Hilbert $2$ -class field tower of some abelian $2$ -extensions over the field of rational numbers

Abdelmalek Azizi, Ali Mouhib (2013)

Czechoslovak Mathematical Journal

It is well known by results of Golod and Shafarevich that the Hilbert $2$ -class field tower of any real quadratic number field, in which the discriminant is not a sum of two squares and divisible by eight primes, is infinite. The aim of this article is to extend this result to any real abelian $2$ -extension over the field of rational numbers. So using genus theory, units of biquadratic number fields and norm residue symbol, we prove that for every real abelian $2$ -extension over $ℚ$ in which eight primes...

On the Hilbert $2$ -class field tower of some imaginary biquadratic number fields

Mohamed Mahmoud Chems-Eddin, Abdelmalek Azizi, Abdelkader Zekhnini, Idriss Jerrari (2021)

Czechoslovak Mathematical Journal

Let $𝕜 = ℚ (\sqrt{2}, \sqrt{d})$ be an imaginary bicyclic biquadratic number field, where $d$ is an odd negative square-free integer and $𝕜_{2}^{(2)}$ its second Hilbert $2$ -class field. Denote by $G = Gal (𝕜_{2}^{(2)} / 𝕜)$ the Galois group of $𝕜_{2}^{(2)} / 𝕜$ . The purpose of this note is to investigate the Hilbert $2$ -class field tower of $𝕜$ and then deduce the structure of $G$ .

On the Hilbert symbol in cyclotomic fields

Charles Helou (2002)

Acta Arithmetica

On the Holomorphic Differential Forms of the Siegel Modular Variety II.

Riccardo Salvati Manni (1990)

Mathematische Zeitschrift

On the Holomorphy on Certain Non-Abelian L-Series.

David Goss (1985)

Mathematische Annalen

On the homology of the special linear group ove a number field.

Dominique Arlettaz (1986)

Commentarii mathematici Helvetici

On the homomorphisms of a family of finite rings

Dimitrios Poulakis (1989)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

On the Homomorphisms of the Integral Linear Groups.

Alexander J. Hahn (1972)

Mathematische Annalen

On the hybrid mean value of Cochrane sums and generalized Kloosterman sums

Tingting Wang (2012)

Acta Arithmetica

On the hybrid mean value of Dedekind sums and Hurwitz zeta-function

Wenpeng Zhang (2000)

Acta Arithmetica

On the ideal class groups of the maximal real subfields of number fields with all roots of unity

Masato Kurihara (1999)

Journal of the European Mathematical Society

In this paper, for a totally real number field $k$ we show the ideal class group of $k {(\cup_{n > 0} μ_{n})}^{+}$ is trivial. We also study the $p$ -component of the ideal class group of the cyclotomic $𝐙_{p}$ -extension.

On the identities of symmetry for the generalized Bernoulli polynomials attached to $χ$ of higher order.

Kim, Taekyun, Jang, Lee-Chae, Kim, Young-Hee, Hwang, Kyung-Won (2009)

Journal of Inequalities and Applications [electronic only]

On the identities of symmetry for the $ζ$ -Euler polynomials of higher order.

Kim, Taekyun, Park, Kyoung Ho, Hwang, Kyung-Won (2009)

Advances in Difference Equations [electronic only]

On the image of $l$ -adic Galois representations for abelian varieties of type I and II.

Banaszak, G., Gajda, W., Krasoń, P. (2007)

Documenta Mathematica

On the image of $Λ$ -adic Galois representations

Ami Fischman (2002)

Annales de l’institut Fourier

We explore the question of how big the image of a Galois representation attached to a $Λ$ -adic modular form with no complex multiplication is and show that for a “generic” set of $Λ$ -adic modular forms (normalized, ordinary eigenforms with no complex multiplication), all have a large image.

On the imbeddings of imaginary quadratic orders in definite quaternion orders.

M. Eichler, J. Brzezinski (1992)

Journal für die reine und angewandte Mathematik

On the incongruence of consecutive fourth powers.

J. Steinig, P. Schumer (1988)

Elemente der Mathematik

On the independence of σ(ϕ(n)) and ϕ(σ(n))

Mohand-Ouamar Hernane, Florian Luca (2009)

Acta Arithmetica

On the index of an odd perfect number

Feng-Juan Chen, Yong-Gao Chen (2014)

Colloquium Mathematicae

Suppose that N is an odd perfect number and $q^{α}$ is a prime power with $q^{α} | | N$ . Define the index $m = σ (N / q^{α}) / q^{α}$ . We prove that m cannot take the form $p^{2 u}$ , where u is a positive integer and 2u+1 is composite. We also prove that, if q is the Euler prime, then m cannot take any of the 30 forms q₁, q₁², q₁³, q₁⁴, q₁⁵, q₁⁶, q₁⁷, q₁⁸, q₁q₂, q₁²q₂, q₁³q₂, q₁⁴ q₂, q₁⁵q₂, q₁²q₂², q₁³q₂², q₁⁴q₂², q₁q₂q₃, q₁²q₂q₃, q₁³q₂q₃, q₁⁴q₂q₃, q₁²q₂²q₃, q₁²q₂²q₃², q₁q₂q₃q₄, q₁²q₂q₃q₄, q₁³q₂q₃q₄, q₁²q₂²q₃q₄, q₁q₂q₃q₄q₅, q₁²q₂q₃q₄q₅, q₁q₂q₃q₄q₅q₆,...

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