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1
Content available remote

On sums involving reciprocals of the largest prime factor of an integer II

100%
Ivić A.
Acta Arithmetica
|
1995
|
tom 71
|
nr 3
229-251
2
Content available remote

On some conjectures and results for the Riemann zeta-function and Hecke series

100%
Ivić A.
Acta Arithmetica
|
2001
|
tom 99
|
nr 2
115-145
3
Content available remote

On some problems involving Hardy’s function

100%
Ivić A.
Open Mathematics
|
2010
|
tom 8
|
nr 6
1029-1040
EN
Some problems involving the classical Hardy function $$ Z\left( t \right) = \zeta \left( {\frac{1} {2} + it} \right)\left( {\chi \left( {\frac{1} {2} + it} \right)} \right)^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} , \zeta \left( s \right) = \chi \left( s \right) \zeta \left( {1 - s} \right) $$, are discussed. In particular we discuss the odd moments of Z(t) and the distribution of its positive and negative values.
4
Content available remote

On the riemann zeta-function and the divisor problem

100%
Ivić A.
Open Mathematics
|
2004
|
tom 2
|
nr 4
494-508
EN
Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of $$\left| {\varsigma \left( {\tfrac{1}{2} + it} \right)} \right|$$ . If $$E^* \left( t \right) = E\left( t \right) - 2\pi \Delta ^* \left( {t / 2\pi } \right)$$ with $$\Delta ^* \left( x \right) = - \Delta \left( x \right) + 2\Delta \left( {2x} \right) - \tfrac{1}{2}\Delta \left( {4x} \right)$$ , then we obtain $$\int_0^T {\left( {E^* \left( t \right)} \right)^4 dt \ll _e T^{16/9 + \varepsilon } } $$ . We also show how our method of proof yields the bound $$\sum\limits_{r = 1}^R {\left( {\int_{tr - G}^{tr + G} {\left| {\varsigma \left( {\tfrac{1}{2} + it} \right)} \right|^2 dt} } \right)^4 \ll _e T^{2 + e} G^{ - 2} + RG^4 T^\varepsilon } $$ , where T 1/5+ε≤G≪T, T
5
Content available remote

Power moments of the error term in the approximate functional equation for ζ²(s)

100%
Ivić A.
Acta Arithmetica
|
1993
|
tom 65
|
nr 2
137-145
6
Content available remote

On the riemann zeta-function and the divisor problem II

100%
Ivić A.
Open Mathematics
|
2005
|
tom 3
|
nr 2
203-214
EN
Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of $$\left| {\zeta \left( {\frac{1}{2} + it} \right)} \right|$$ . If E *(t)=E(t)-2πΔ*(t/2π) with $$\Delta *\left( x \right) + 2\Delta \left( {2x} \right) - \frac{1}{2}\Delta \left( {4x} \right)$$ , then we obtain $$\int_0^T {\left| {E*\left( t \right)} \right|^5 dt} \ll _\varepsilon T^{2 + \varepsilon } $$ and $$\int_0^T {\left| {E*\left( t \right)} \right|^{\frac{{544}}{{75}}} dt} \ll _\varepsilon T^{\frac{{601}}{{225}} + \varepsilon } .$$ It is also shown how bounds for moments of | E *(t)| lead to bounds for moments of $$\left| {\zeta \left( {\frac{1}{2} + it} \right)} \right|$$ .
7
Content available remote

On some mean value results for the zeta-function in short intervals

100%
Ivić A.
Acta Arithmetica
|
2014
|
tom 162
|
nr 2
141-158
EN
Let $Δ(x)$ denote the error term in the Dirichlet divisor problem, and let E(T) denote the error term in the asymptotic formula for the mean square of |ζ(1/2+it)|. If E*(t) := E(t) - 2πΔ*(t/(2π)) with Δ*(x) = -Δ(x) + 2Δ(2x) - 1/2Δ(4x) and $∫_0^T E*(t) dt = 3/4πT + R(T)$, then we obtain a number of results involving the moments of |ζ(1/2+it)| in short intervals, by connecting them to the moments of E*(T) and R(T) in short intervals. Upper bounds and asymptotic formulae for integrals of the form ∫_T^{2T}(∫_{t-H}^{t+H} |ζ(1/2+iu|^2 du}^k dt$ (k ∈ ℕ, 1 ≪ H ≤ T) are also treated.
8
Content available remote

Sums of coefficients of Hecke series

64%
Ivić A., Meurman T.
Acta Arithmetica
|
1994
|
tom 68
|
nr 4
341-368
9
Content available remote

The Mellin transform of powers of the zeta-function

52%
Ivić A., Jutila M., Motohashi Y.
Acta Arithmetica
|
2000
|
tom 95
|
nr 4
305-342
10
Content available remote

On some estimates involving the number of prime divisors of an integer

44%
Ivić A.
Acta Arithmetica
|
1987-1988
|
tom 49
|
nr 1
21-33
11
Content available remote

Some new estimates in the Dirichlet divisor problem

38%
Ivić A., Ouellet M.
Acta Arithmetica
|
1989
|
tom 52
|
nr 3
241-253
12
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Content available

A theorem in asymptotic number theory

38%
Ivić A.
Colloquium Mathematicum
|
1978
|
tom 39
|
nr 1
177-184
13
Content available remote

Large values of certain number-theoretic error terms

38%
Ivić A.
Acta Arithmetica
|
1990
|
tom 56
|
nr 2
135-159
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