All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 55 Next

Displaying 1081 – 1100 of 3028

Showing per page

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 ∑ n ≥ 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 L -functions of G L ( 2 ) × 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 ) × 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 ≡ 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 · 3 R - 1 · 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 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.

Currently displaying 1081 – 1100 of 3028