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Displaying 81 – 100 of 370

Gauss–Manin connections for $p$ -adic families of nearly overconvergent modular forms

Robert Harron, Liang Xiao (2014)

Annales de l’institut Fourier

We interpolate the Gauss–Manin connection in $p$ -adic families of nearly overconvergent modular forms. This gives a family of Maass–Shimura type differential operators from the space of nearly overconvergent modular forms of type $r$ to the space of nearly overconvergent modular forms of type $r + 1$ with $p$ -adic weight shifted by $2$ . Our construction is purely geometric, using Andreatta–Iovita–Stevens and Pilloni’s geometric construction of eigencurves, and should thus generalize to higher rank groups.

Gauss's ₂F₁ hypergeometric function and the congruent number elliptic curve

Ahmad El-Guindy, Ken Ono (2010)

Acta Arithmetica

Gauss's three squares theorem with almost prime variables

Guangshi Lü (2007)

Acta Arithmetica

GCD of truncated rows in Pascal's triangle.

Kaplan, Gil, Levy, Dan (2004)

Integers

GCD sums from Poisson integrals and systems of dilated functions

Christoph Aistleitner, István Berkes, Kristian Seip (2015)

Journal of the European Mathematical Society

Upper bounds for GCD sums of the form $\sum_{k, ℓ = 1}^{N} \frac{{(\gcd (n_{k}, n_{ℓ}))}^{2 α}}{{(n_{k} n_{ℓ})}^{α}}$ are established, where ${(n_{k})}_{1 \leq k \leq N}$ is any sequence of distinct positive integers and $0 < α \leq 1$ ; the estimate for $α = 1 / 2$ solves in particular a problem of Dyer and Harman from 1986, and the estimates are optimal except possibly for $α = 1 / 2$ . The method of proof is based on identifying the sum as a certain Poisson integral on a polydisc; as a byproduct, estimates for the largest eigenvalues of the associated GCD matrices are also found. The bounds for such GCD sums are used to establish...

Gcd-closed sets and determinants of matrices associated with arithmetical functions

Shaofang Hong (2002)

Acta Arithmetica

Gedämpfte zahlentheoretische Transformationen.

Fritz Schweiger (1975)

Monatshefte für Mathematik

Gelöste und ungelöste Fragen über Basen der natürlichen Zahlenreihe. I.

Alfred Stöhr (1955)

Journal für die reine und angewandte Mathematik

Gelöste und ungelöste Fragen über Basen der natürlichen Zahlenreihe. II.

Alfred Stöhr (1955)

Journal für die reine und angewandte Mathematik

Genera of arithmetic Fuchsian groups

Stefan Johansson (1998)

Acta Arithmetica

Genera of congruence subgroups in Q-quaternion algebras.

David A. Cox, Walter R. Parry (1984)

Journal für die reine und angewandte Mathematik

General Dirichlet series, arithmetic convolution equations and Laplace transforms

Helge Glöckner, Lutz G. Lucht, Štefan Porubský (2009)

Studia Mathematica

In the earlier paper [Proc. Amer. Math. Soc. 135 (2007)], we studied solutions g: ℕ → ℂ to convolution equations of the form $a_{d} * g^{* d} + a_{d - 1} * g^{* (d - 1)} + \dots + a ₁ * g + a ₀ = 0$ , where $a ₀, . . ., a_{d} : ℕ \to ℂ$ are given arithmetic functions associated with Dirichlet series which converge on some right half plane, and also g is required to be such a function. In this article, we extend our previous results to multidimensional general Dirichlet series of the form $\sum_{x \in X} f (x) e^{- s x}$ ( $s \in ℂ^{k}$ ), where $X \subseteq {[0, \infty)}^{k}$ is an additive subsemigroup. If X is discrete and a certain solvability criterion is satisfied,...

Currently displaying 81 – 100 of 370

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Displaying 81 – 100 of 370

Gauss–Manin connections for $p$ -adic families of nearly overconvergent modular forms

Gauss's ₂F₁ hypergeometric function and the congruent number elliptic curve

Gauss's three squares theorem with almost prime variables

GCD of truncated rows in Pascal's triangle.

GCD sums from Poisson integrals and systems of dilated functions

Gcd-closed sets and determinants of matrices associated with arithmetical functions

Gedämpfte zahlentheoretische Transformationen.

Gelöste und ungelöste Fragen über Basen der natürlichen Zahlenreihe. I.

Gelöste und ungelöste Fragen über Basen der natürlichen Zahlenreihe. II.

Genera of arithmetic Fuchsian groups

Genera of congruence subgroups in Q-quaternion algebras.

General Dirichlet series, arithmetic convolution equations and Laplace transforms

General discrepancy estimates II: the Haar function system

General Discrepancy Estimates III: The Erdös-Turán-Koksma Inequality for the Haar Function System.

General discrepancy estimates: the Walsh function system

General $gcd$ -product function.

General multiplicative functions

General properties involving reciprocals of binomial coefficients.

Généralisation de la multiplication de Fibonacci

Généralisation de la théorie des fractions continues

Currently displaying 81 – 100 of 370