On zeta function identities involving sums of squares and the zeta–theta correspondence
نویسندگان
چکیده
منابع مشابه
On Sums of Squares of the Riemann Zeta-function on the Critical Line
and some related integrals, where γ denotes imaginary parts of complex zeros of ζ(s), and where every zero is counted with its multiplicity (see also [5] and [7]). The interest is in obtaining unconditional bounds for the above sum, since assuming the Riemann Hypothesis (RH) the sum trivially vanishes. A more general sum than the one in (1.1) was treated by S.M. Gonek [3]. He proved, under the ...
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Partition Identities for the Multiple Zeta Function
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Several identities for the Riemann zeta-function ζ(s) are proved. For example, if s = σ + it and σ > 0, then ∞ −∞ (1 − 2 1−s)ζ(s) s 2 dt = π σ (1 − 2 1−2σ)ζ(2σ). Let as usual ζ(s) = ∞ n=1 n −s (ℜe s > 1) denote the Riemann zeta-function. The motivation for this note is the quest to evaluate explicitly integrals of |ζ(1 2 + it)| 2k , k ∈ N, weighted by suitable functions. In particular, the prob...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2011
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2011.02.016