Pair correlation of the zeros of the Riemann zeta function in longer ranges
Tsz Ho Chan (2004)
Acta Arithmetica
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Displaying similar documents to “On theta type functions associated with the zeros of the Selberg zeta functions.”
Pair correlation of the zeros of the Riemann zeta function in longer ranges
On an asymptotic formula of Ramanujan for a certain theta-type series
Masanori Katsurada (2001)
Acta Arithmetica
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A note on the zeros of the derivative of the Riemann zeta function near the critical line
Shaoji Feng (2005)
Acta Arithmetica
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The distribution of zeros of Epstein zeta functions over GLₙ
Riad Masri (2007)
Acta Arithmetica
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A zero density result for the Riemann zeta function
Habiba Kadiri (2013)
Acta Arithmetica
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We prove an explicit bound for N(σ,T), the number of zeros of the Riemann zeta function satisfying ℜ𝔢 s ≥ σ and 0 ≤ ℑ𝔪 s ≤ T. This result provides a significant improvement to Rosser's bound for N(T) when used for estimating prime counting functions.
Large gaps between consecutive zeros of the Riemann zeta-function. II
H. M. Bui (2014)
Acta Arithmetica
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Assuming the Riemann Hypothesis we show that there exist infinitely many consecutive zeros of the Riemann zeta-function whose gaps are greater than 2.9 times the average spacing.
Pair correlation of zeros of the zeta function.
P.X. Gallagher (1985)
Journal für die reine und angewandte Mathematik
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Simple zeros of the zeta function of a quadratic number field. I.
S.M. Gonek, J.B. Conrey, A. Ghosh (1986)
Inventiones mathematicae
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Zeros of the Riemann Zeta-function on the critical line.
D.R. Heath-Brown (1993)
Mathematische Zeitschrift
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Gaps between primes, and the pair correlation of zeros of the zeta-function
D. Heath-Brown (1982)
Acta Arithmetica
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More than 41% of the zeros of the zeta function are on the critical line
H. M. Bui, Brian Conrey, Matthew P. Young (2011)
Acta Arithmetica
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Asymptotic expansions of certain q-series and a formula of Ramanujan for specific values of the Riemann zeta function
Masanori Katsurada (2003)
Acta Arithmetica
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A note on moments of .
Laurinčikas, Antanas, Steuding, Jörn (2004)
Publications de l'Institut Mathématique. Nouvelle Série
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Extreme values of the Riemann zeta-function on short zero intervals
R. R. Hall (2006)
Acta Arithmetica
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Selberg Zeta function on an exceptional domain.
Henry H. Kim (1994)
Manuscripta mathematica
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A functional relation for Tornheim's double zeta functions
Kazuhiro Onodera (2014)
Acta Arithmetica
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We generalize the partial fraction decomposition which is fundamental in the theory of multiple zeta values, and prove a relation between Tornheim's double zeta functions of three complex variables. As applications, we give new integral representations of several zeta functions, an extension of the parity result to the whole domain of convergence, concrete expressions of Tornheim's double zeta function at non-positive integers and some results on the behavior of a certain Witten's zeta...