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Displaying 1081 – 1100 of 3028

On $p$ -adic Euler constants

Abhishek Bharadwaj (2021)

Czechoslovak Mathematical Journal

The goal of this article is to associate a $p$ -adic analytic function to the Euler constants $γ_{p} (a, F)$ , study the properties of these functions in the neighborhood of $s = 1$ and introduce a $p$ -adic analogue of the infinite sum $\sum_{n \geq 1} f (n) / n$ for an algebraic valued, periodic function $f$ . After this, we prove the theorem of Baker, Birch and Wirsing in this setup and discuss irrationality results associated to $p$ -adic Euler constants generalising the earlier known results in this direction. Finally, we define and prove certain...

On $p$ -adic geometric representations of $G_{ℚ}$ .

Wintenberger, J.-P. (2007)

Documenta Mathematica

On $p$ -adic $L$ -functions

John Coates (1988/1989)

Séminaire Bourbaki

On $p$ -adic $L$ -functions and the Riemann-Hurwitz genus formula

Warren M. Sinnott (1984)

Compositio Mathematica

On $p$ -adic $L$ -functions of $G L (2) \times G L (2)$ over totally real fields

Haruzo Hida (1991)

Annales de l'institut Fourier

Let $D (s, f, g)$ be the Rankin product $L$ -function for two Hilbert cusp forms $f$ and $g$ . This $L$ -function is in fact the standard $L$ -function of an automorphic representation of the algebraic group $G L (2) \times G L (2)$ defined over a totally real field. Under the ordinarity assumption at a given prime $p$ for $f$ and $g$ , we shall construct a $p$ -adic analytic function of several variables which interpolates the algebraic part of $D (m, f, g)$ for critical integers $m$ , regarding all the ingredients $m$ , $f$ and $g$ as variables.

On $p$ -adic zeros of systems of diagonal forms restricted by a congruence condition

Hemar Godhino, Paulo H. A. Rodrigues (2007)

Journal de Théorie des Nombres de Bordeaux

This paper is concerned with non-trivial solvability in $p$ -adic integers of systems of additive forms. Assuming that the congruence equation $a x^{k} + b y^{k} + c z^{k} \equiv d (m o d p)$ has a solution with $x y z ≢ 0 (m o d p)$ we have proved that any system of $R$ additive forms of degree $k$ with at least $2 \cdot 3^{R - 1} \cdot k + 1$ variables, has always non-trivial $p$ -adic solutions, provided $p ∤ k$ . The assumption of the solubility of the above congruence equation is guaranteed, for example, if $p > k^{4}$ .

On p-adic analogues of the conjectures of Birch and Swinnerton-Dyer.

B. Mazur, J. Tate, J. Teitelbaum (1986)

Inventiones mathematicae

On p-adic L-functions and normal bases of rings of integers.

Humio Ichimura (1995)

Journal für die reine und angewandte Mathematik

On p-adic L-functions and the Riemann-Hurwitz genus formula

Sang G. Han (1991)

Acta Arithmetica

On p-adic L-functions Associated to Elliptic Curves.

Stephen Lichtenbaum (1980)

Inventiones mathematicae

On p-Adic L-Functions over Real Quadratic Fields.

J. Coates, W. Sinnot (1974)

Inventiones mathematicae

On p-Adic Power Series.

Paul Monsky (1981)

Mathematische Annalen

On p-adic Siegel modular forms of non-real Nebentypus

Toshiyuki Kikuta (2012)

Acta Arithmetica

On p-adic Siegel-Eisenstein series of weight k

Yoshinori Mizuno (2008)

Acta Arithmetica

On pairings of the first 2n natural numbers

G. Huff (1973)

Acta Arithmetica

On pairs of additive cubic equations.

R.C. Baker, J. Brüdern (1988)

Journal für die reine und angewandte Mathematik

On pairs of binary forms with given resultant or given semi-resultant.

Györy, K. (1993)

Mathematica Pannonica

On pairs of closed geodesics on hyperbolic surfaces

Nigel J. E. Pitt (1999)

Annales de l'institut Fourier

In this article we prove a trace formula for double sums over totally hyperbolic Fuchsian groups $Γ$ . This links the intersection angles and common perpendiculars of pairs of closed geodesics on $Γ / H$ with the inner products of squares of absolute values of eigenfunctions of the hyperbolic laplacian $Δ$ . We then extract quantitative results about the intersection angles and common perpendiculars of these geodesics both on average and individually.

On pairs of Goldbach-Linnik equations with unequal powers of primes

Enxun Huang (2023)

Czechoslovak Mathematical Journal

It is proved that every pair of sufficiently large odd integers can be represented by a pair of equations, each containing two squares of primes, two cubes of primes, two fourth powers of primes and 105 powers of 2.

On pairs of linear equations in three prime variables and an application to Goldbach's problem.

Ming-Chit Liu, Kai-Man Tsang (1989)

Journal für die reine und angewandte Mathematik

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