On Wild Frieze Patterns
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DOI: 10.1080/10586458.2016.1172526
Abstract: ABSTRACT In this article, among other things, we show: (1) There are periodic wild -frieze patterns whose entries are positive integers. (2) There are non-periodic -frieze patterns whose entries are positive integers. (3) There is… read more here.
Keywords: frieze patterns; entries positive; whose entries; wild frieze ... See more keywords
On certain sums concerning the gcd’s and lcm’s of k positive integers
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DOI: 10.1142/s1793042120500049
Abstract: We use elementary arguments to prove results on the order of magnitude of certain sums concerning the gcd’s and lcm’s of [Formula: see text] positive integers, where [Formula: see text] is fixed. We refine and… read more here.
Keywords: gcd lcm; sums concerning; certain sums; positive integers ... See more keywords
Integer-valued definable functions in ℝan,exp
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DOI: 10.1142/s1793042121500597
Abstract: We give two variations on a result of Wilkie’s [A. J. Wilkie, Complex continuations of [Formula: see text]-definable unary functions with a diophantine application, J. Lond. Math. Soc. (2) 93(3) (2016) 547–566] on unary functions definable… read more here.
Keywords: integer; positive integers; formula see; integer valued ... See more keywords
On values of the higher derivatives of the Barnes zeta function at non-positive integers
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DOI: 10.2996/kmj/kmj45105
Abstract: Let x be a complex number which has a positive real part, and w_1,...,w_N be positive rational numbers. We write w^s \zeta_N (s, x | w_1,...,w_N) as a finite linear combination of the Hurwitz zeta… read more here.
Keywords: function; non positive; barnes zeta; zeta function ... See more keywords