On $t$-adic Littlewood conjecture for certain infinite products

Productly linearly independent sequences

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/012.2015.52.3.1315 ◽

2015 ◽

Vol 52 (3) ◽

pp. 350-370

Author(s):

Jaroslav Hančl ◽

Katarína Korčeková ◽

Lukáš Novotný

Keyword(s):

Rational Numbers ◽

Infinite Products ◽

Linearly Independent ◽

New Concepts ◽

Infinite Sequences

We introduce the two new concepts, productly linearly independent sequences and productly irrational sequences. Then we prove a criterion for which certain infinite sequences of rational numbers are productly linearly independent. As a consequence we obtain a criterion for the irrationality of infinite products and a criterion for a sequence to be productly irrational.

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An unresolved analogue of the Littlewood Conjecture

Involve a Journal of Mathematics ◽

10.2140/involve.2010.3.191 ◽

2010 ◽

Vol 3 (2) ◽

pp. 191-196

Author(s):

Clarice Ferolito

Keyword(s):

Littlewood Conjecture

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New Infinite Products of Cosines and Viète-Like Formulae

Mathematics Magazine ◽

10.4169/math.mag.86.1.015 ◽

2013 ◽

Vol 86 (1) ◽

pp. 15-25 ◽

Cited By ~ 3

Author(s):

Samuel G. Moreno ◽

Esther M. García

Keyword(s):

Infinite Products

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Discussions: Relating to Infinite Products for sinz and cosz

American Mathematical Monthly ◽

10.2307/2974334 ◽

1917 ◽

Vol 24 (5) ◽

pp. 246 ◽

Cited By ~ 1

Author(s):

M. B. Porter

Keyword(s):

Infinite Products

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Weak convergence of infinite products of operators in Hadamard spaces

Rendiconti del Circolo Matematico di Palermo (1952 -) ◽

10.1007/s12215-015-0218-6 ◽

2015 ◽

Vol 65 (1) ◽

pp. 55-71 ◽

Cited By ~ 23

Author(s):

Simeon Reich ◽

Zuly Salinas

Keyword(s):

Weak Convergence ◽

Infinite Products

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Maclaurin's type infinite products involving certain transcendental functions

Tbilisi Mathematical Journal ◽

10.32513/tmj/1932200817 ◽

2021 ◽

Vol 14 (1) ◽

Author(s):

Mohammad Idris Qureshi ◽

Mahvish Ali ◽

Dilshad Ahamad ◽

Saima Jabee

Keyword(s):

Infinite Products ◽

Transcendental Functions

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A closer look at some new identities

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171298000805 ◽

1998 ◽

Vol 21 (3) ◽

pp. 581-586

Author(s):

Geoffrey B. Campbell

Keyword(s):

Positive Integer ◽

Infinite Products ◽

Integer Solutions ◽

Origin Point

We obtain infinite products related to the concept of visible from the origin point vectors. Among these is∏k=3∞(1−Z)φ,(k)/k=11−Zexp(Z32(1−Z)2−12Z−12Z(1−Z)), |Z|<1,in whichφ3(k)denotes for fixedk, the number of positive integer solutions of(a,b,k)=1wherea<b<k, assuming(a,b,k)is thegcd(a,b,k).

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