Remarks on Weil’s quadratic functional in the theory of prime numbers, I

Enrico Bombieri

Displaying similar documents to “Remarks on Weil’s quadratic functional in the theory of prime numbers, I”

On general L-functions

E. Carletti, G. Monti Bragadin, A. Perelli (1994)

Acta Arithmetica

Similarity:

A lower bound for the zeros of Riemann's zeta function on the critical line

Enrico Bombieri (1974-1975)

Séminaire Bourbaki

Similarity:

On sign-changes in the remainder-term of the prime-number formula, II

Jerzy Kaczorowski (1985)

Acta Arithmetica

Similarity:

On differences of two squares

Manfred Kühleitner, Werner Nowak (2006)

Open Mathematics

Similarity:

The arithmetic function ρ(n) counts the number of ways to write a positive integer n as a difference of two squares. Its average size is described by the Dirichlet summatory function Σn≤x ρ(n), and in particular by the error term R(x) in the corresponding asymptotics. This article provides a sharp lower bound as well as two mean-square results for R(x), which illustrates the close connection between ρ(n) and the number-of-divisors function d(n).

A note on the distribution of primes

A. Ingham (1935)

Acta Arithmetica

Similarity:

Abundant numbers and the Riemann hypothesis.

Briggs, Keith (2006)

Experimental Mathematics

Similarity:

On the density of the zeros of the Dedekind Zeta-function

D. Heath-Brown (1977)

Acta Arithmetica

Similarity:

Riemann's Hypothesis

Rusev, Peter (2010)

Union of Bulgarian Mathematicians

Similarity:

Riemann’s memoir is devoted to the function π(x) defined as the number of prime numbers less or equal to the real and positive number x. This is really the fact, but the “main role” in it is played by the already mentioned zeta-function.

Some problems on mean values of the Riemann zeta-function

Aleksandar Ivić (1996)

Journal de théorie des nombres de Bordeaux

Similarity:

Several problems and results on mean values of $ζ (s)$ are discussed. These include mean values of $| ζ (\frac{1}{2} + i t) |$ and the fourth moment of $| ζ (σ + i t) |$ for $1 / 2 < σ < 1$ .