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A front row seat to the work of Aleksandar Ivić
(Beograd : Académie Serbe des sciences et des arts, 2021)
We provide a survey of the vast contribution of Aleksandar Ivic´ to analytic
number theory. Emphasis is put on Ivic´’s work on arithmetical functions. Highlights of his
contribution to the study of the Riemann zeta-function ...
Summation of slowly convergent series by Gaussian type of quadratures and application to calculation of values of the Riemann zeta function
(Beograd : Académie Serbe des sciences et des arts, 2021)
Beside a short account on the summation/integration methods for slowly
convergent series (Laplace transform method for numerical and trigonometric series and the
method of contour integration over a rectangle), a method ...
Incomplete Kloosterman sums to prime power modules
(Beograd : Académie Serbe des sciences et des arts, 2021)
We prove that for prime p, p → +∞, integer r ! 4 and q = pr an
incomplete Kloosterman sum of length N to modulus q can be estimated non-trivially (with
power-saving factor) for very small N, namely, for N ≫ (q log q)1/(r−1)
.
Fifty years of Kurepa’s !n hypothesis
(Beograd : Académie Serbe des sciences et des arts, 2021)
Djuro Kurepa formulated in 1971 the so called left factorial hypothesis.
This hypothesis is still open, despite much efforts to solve it. Here we give some historical
notes and review the current status of the hypothesis. ...
Gutman index – a critical personal account
(Beograd : Académie Serbe des sciences et des arts, 2021)
In the recent literature there are numerous publications concerned with a
graph invariant named “Gutman index” (ZZ). In this paper, some details about the discovery
of ZZ are explained. In particular, it is pointed out ...
On some integrals involving ∆2(x) and ∆3(x)
(Beograd : Académie Serbe des sciences et des arts, 2021)
Let k ≥ 2 be a fixed natural number and dk(n) denote the number of
ways n can be written as a product of k positive integers. Let ∆k(x) denote the error term
in the asymptotic formula of the summatory function of dk(n). ...
In Memorium: Aleksandar Ivić (March 6, 1949 – December 27, 2020)
(Beograd : Académie Serbe des sciences et des arts, 2021)
Eminent scientist Aleksandar Sanja Ivić, Full Member of the Serbian Academy of Sciences and Arts (SANU), passed away on December 27, 2020, after a vicious illness he faced with an unprecedented will, but unfortunately he ...
Two Perov type generalized graph contractions
(Beograd : Académie Serbe des sciences et des arts, 2021)
In [Priblizˇ. Metod. Resˇen. Differencial’. Uravnen. 2 (1964), 115 − 134]
A. I. Perov generalized the Banach contraction principle by employing matrices instead of
contraction constants. In this paper, we introduce and ...
Boundary values, integral transforms, and growth of vector valued Hardy functions
(Beograd : Académie Serbe des sciences et des arts, 2021)
Banach space valued Hardy functions Hp, 0 < p ≤ ∞, are defined
with the functions having domain in tubes T C = Rn + iC ⊂ Cn; H2 functions with values
in Hilbert space are characterized as Fourier-Laplace transforms of ...
Miscellaneous formulae for the certain class of combinatorial sums
(Beograd : Académie Serbe des sciences et des arts, 2021)
In a recent paper [Montes Taurus J. Pure Appl. Math. 3 (1) (2021), 38–61]
we defined the class of combinatorial sums.
The purpose of this paper is to give some integral formulas, identities and combinatorial
sums using ...