Displaying similar documents to “Multiple zeta values and periods of moduli spaces 𝔐 ¯ 0 , n ”

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

Ramūnas Garunkštis, Andrius Grigutis (2019)

Czechoslovak Mathematical Journal

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Let ζ ( s ) be the Riemann zeta-function. If t ≥ 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 - s ¯ ) | > | L ( λ , λ , s ) | .

Moduli of smoothness of functions and their derivatives

Z. Ditzian, S. Tikhonov (2007)

Studia Mathematica

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Relations between moduli of smoothness of the derivatives of a function and those of the function itself are investigated. The results are for L p ( T ) and L p [ - 1 , 1 ] for 0 < p < ∞ using the moduli of smoothness ω r ( f , t ) p and ω φ r ( f , t ) p respectively.

Some infinite sums identities

Meher Jaban, Sinha Sneh Bala (2015)

Czechoslovak Mathematical Journal

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We find the sum of series of the form ∑ i = 1 ∞ f ( i ) i r for some special functions f . The above series is a generalization of the Riemann zeta function. In particular, we take f as some values of Hurwitz zeta functions, harmonic numbers, and combination of both. These generalize some of the results given in Mező’s paper (2013). We use multiple zeta theory to prove all results. The series sums we have obtained are in terms of Bernoulli numbers and powers of π .

Dirichlet series induced by the Riemann zeta-function

Jun-ichi Tanaka (2008)

Studia Mathematica

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The Riemann zeta-function ζ(s) extends to an outer function in ergodic Hardy spaces on ω , the infinite-dimensional torus indexed by primes p. This enables us to investigate collectively certain properties of Dirichlet series of the form ( a p , s ) = ∏ p ( 1 - a p p - s ) - 1 for a p in ω . Among other things, using the Haar measure on ω for measuring the asymptotic behavior of ζ(s) in the critical strip, we shall prove, in a weak sense, the mean-value theorem for ζ(s), equivalent to the Lindelöf hypothesis.

On the spinor zeta functions problem: higher power moments of the Riesz mean

Haiyan Wang (2013)

Acta Arithmetica

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Let F be a Siegel cusp form of integral weight k on the Siegel modular group Sp₂(ℤ) of genus 2. The coefficients of the spinor zeta function Z F ( s ) are denoted by cₙ. Let D ρ ( x ; Z F ) be the Riesz mean of cₙ. Kohnen and Wang obtained the truncated Voronoï-type formula for D ρ ( x ; Z F ) under the Ramanujan-Petersson conjecture. In this paper, we study the higher power moments of D ρ ( x ; Z F ) , and then derive an asymptotic formula for the hth (h=3,4,5) power moments of D ₁ ( x ; Z F ) by using Ivić’s large value arguments and other techniques. ...