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Let $ζ (s)$ be the Riemann zeta-function. If $t \geq 6.8$ and $σ > 1 / 2$ , then it is known that the inequality $| ζ (1 - s) | > | ζ (s) |$ is valid except at the zeros of $ζ (s)$ . Here we investigate the Lerch zeta-function $L (λ, α, s)$ which usually has many zeros off the critical line and it is expected that these zeros are asymmetrically distributed with respect to the critical line. However, for equal parameters $λ = α$ it is still possible to obtain a certain version of the inequality $| L (λ, λ, 1 - \bar{s}) | > | L (λ, λ, s) |$ .

Théorie des nombres et singularités.

Pierrette CASSOU-NOGUÊS (1983/1984)

Seminaire de Théorie des Nombres de Bordeaux

Displaying 1 – 7 of 7

The Adelic Zeta Function Associated to the Space of Binary Cubis Forms. Part I: Global Theory.

The average order of a class of arithmetic functions over arithmetic progressions with applications to quadratic forms.

The Generalized Divisor Problem Over Arithmetic Progressions.

The number of primes in a short interval.

The Selberg zeta function and a local trace formula for Kleinian groups.

The size of the Lerch zeta-function at places symmetric with respect to the line ℜ ( s ) = 1 / 2

Théorie des nombres et singularités.

Currently displaying 1 – 7 of 7

The size of the Lerch zeta-function at places symmetric with respect to the line $ℜ (s) = 1 / 2$