منابع مشابه
On the distribution of zeros of the Hurwitz zeta-function
Assuming the Riemann hypothesis, we prove asymptotics for the sum of values of the Hurwitz zeta-function ζ(s, α) taken at the nontrivial zeros of the Riemann zeta-function ζ(s) = ζ(s, 1) when the parameter α either tends to 1/2 and 1, respectively, or is fixed; the case α = 1/2 is of special interest since ζ(s, 1/2) = (2s − 1)ζ(s). If α is fixed, we improve an older result of Fujii. Besides, we...
متن کاملSimple Zeros of the Riemann Zeta-function
Assuming the Riemann Hypothesis, Montgomery and Taylor showed that at least 67.25% of the zeros of the Riemann zeta-function are simple. Using Montgomery and Taylor's argument together with an elementary combinatorial argument, we prove that assuming the Riemann Hypothesis at least 67.275% of the zeros are simple.
متن کاملThe Critical Values of Generalizations of the Hurwitz Zeta Function
We investigate a few types of generalizations of the Hurwitz zeta function, written Z(s, a) in this abstract, where s is a complex variable and a is a parameter in the domain that depends on the type. In the easiest case we take a ∈ R, and one of our main results is that Z(−m, a) is a constant times Em(a) for 0 ≤ m ∈ Z, where Em is the generalized Euler polynomial of degree n. In another case, ...
متن کاملIntegral representations of q-analogues of the Hurwitz zeta function
Two integral representations of q-analogues of the Hurwitz zeta function are established. Each integral representation allows us to obtain an analytic continuation including also a full description of poles and special values at non-positive integers of the q-analogue of the Hurwitz zeta function, and to study the classical limit of this qanalogue. All the discussion developed here is entirely ...
متن کاملOn the real roots of the Bernoulli polynomials and the Hurwitz zeta-function
The behaviour of the real roots of the Bernoulli polynomials Bm(a) for large m is investigated. It is shown that if N(m) is the number of these roots then lim m→∞ N(m) m = 2 πe We also show that on the interval Im : − [ m−2 2πe ] < a < 1 + [ m−2 2πe ] , the roots of Bm(a) are close to the half-integer lattices: a = 0,±1/2,±1,±3/2,±2, ... if m is odd, and a = ±1/4,±3/4,±5/4,±7/4, ... if m is eve...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2018
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa8647-11-2017