Falling Operators with Their Connections with the Degenerate Poisson Appell Polynomials: Falling operators with their connections with the degenerate Poisson Appell polynomials

Authors: Riahi, Anis, Rhaima, Mohamed, Ghoudi, Hamza

Source: Complex Analysis and Operator Theory. 19

Subject Terms: Probabilistic potential theory, degenerate falling operators, Appell polynomials, Real polynomials: analytic properties, etc, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Mittag-Leffler functions and generalizations, degenerate Poisson measure, Polynomials in number theory

File Description: application/xml

Access URL: https://zbmath.org/8033590
https://doi.org/10.1007/s11785-025-01673-y

Salem numbers with minimal trace

Authors: Chen, Qiong, Wu, Qiang

Source: Mathematics of Computation. 92:1779-1790

Subject Terms: PV-numbers and generalizations, other special algebraic numbers, Mahler measure, Salem number, integer transfinite diameter, explicit auxiliary function, LLL algorithm, semi-infinite linear programming, Algebraic number theory computations, Chebyshev polynomial, Polynomials in number theory

File Description: application/xml

Access URL: https://zbmath.org/7673303
https://doi.org/10.1090/mcom/3833

THE ABSOLUTE -MEASURE OF TOTALLY POSITIVE ALGEBRAIC INTEGERS: The absolute \(S_k\)-measure of totally positive algebraic integers

Authors: CONG WANG, XIAOJUAN PANG, QIANG WU

Source: Bulletin of the Australian Mathematical Society. 107:239-249

Subject Terms: PV-numbers and generalizations, other special algebraic numbers, Mahler measure, \(S_k\)-measure, explicit auxiliary function, LLL algorithm, semi-infinite linear programming, Algebraic number theory computations, 0101 mathematics, 01 natural sciences, totally positive algebraic integer, Polynomials in number theory

File Description: application/xml

Sur l'irréductibilité d'une classe des polynômes. I

Authors: Györy, K.

Source: Publicationes Mathematicae Debrecen. 18:289-307

Subject Terms: Polynomials in real and complex fields: factorization, 0102 computer and information sciences, 0101 mathematics, 01 natural sciences, Polynomials in general fields (irreducibility, etc.), Polynomials in number theory

File Description: application/xml

Access URL: https://zbmath.org/3396043
https://zbmath.org/3425732

On polynomials with integer coefficients and given discriminant. IV

Authors: Györy, K.

Source: Publicationes Mathematicae Debrecen. 25:155-167

Subject Terms: 0101 mathematics, 01 natural sciences, Polynomials (irreducibility, etc.), Polynomials in number theory, Discriminant of Polynomials

File Description: application/xml

Access URL: https://zbmath.org/3629063

On the relations between the zeros of a polynomial and its Mahler measure

Authors: Ounaïes, Myriam, Rhin, Georges, Sac-Epee, Jean-Marc

Contributors: Sac-Epee, Jean-Marc

Source: Journal of Number Theory. 224:165-190

Subject Terms: Mathematics - Number Theory, Polynomials in real and complex fields: location of zeros (algebraic theorems), 01 natural sciences, estimation of the zeros, Integer polynomials, PV-numbers and generalizations, other special algebraic numbers, Mahler measure, FOS: Mathematics, Number Theory (math.NT), 0101 mathematics, 11C08 11R06, 11C08, 12D10, Algebraic numbers, rings of algebraic integers, Polynomials in number theory, Polynomials (irreducibility, etc.), length of a polynomial, number of real zeros, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]

File Description: application/xml

Access URL: http://arxiv.org/pdf/2103.07126
http://arxiv.org/abs/2103.07126
https://hal.science/hal-03152895v1
https://doi.org/10.1016/j.jnt.2021.01.016
https://zbmath.org/7334485
https://doi.org/10.1016/j.jnt.2021.01.016
http://ui.adsabs.harvard.edu/abs/2021arXiv210307126O/abstract
https://hal.archives-ouvertes.fr/hal-03152895
https://arxiv.org/abs/2103.07126
https://www.sciencedirect.com/science/article/pii/S0022314X21000445
https://arxiv.org/pdf/2103.07126.pdf

Upper bounds for the usual measures of totally positive algebraic integers with house less than 5.8

Authors: V. Flammang

Source: Mathematics of Computation. 90:379-388

Subject Terms: explicit auxiliary functions, PV-numbers and generalizations, other special algebraic numbers, Mahler measure, absolute trace, Algebraic number theory computations, 0101 mathematics, totally positive algebraic integers, 01 natural sciences, absolute length, Polynomials in number theory, absolute Mahler measure

File Description: application/xml

Access URL: https://zbmath.org/7268663
https://doi.org/10.1090/mcom/3580
https://dblp.uni-trier.de/db/journals/moc/moc90.html#Flammang21
https://www.ams.org/mcom/earlyview/#mcom3580/.pdf

An analog to the Schur-Siegel-Smyth trace problem

Authors: V. Flammang

Source: Mathematics of Computation. 89:2387-2398

Subject Terms: explicit auxiliary functions, PV-numbers and generalizations, other special algebraic numbers, Mahler measure, Schur-Siegel-Smyth trace problem, absolute trace, Algebraic number theory computations, 0101 mathematics, totally positive algebraic integers, 01 natural sciences, Polynomials in number theory

File Description: application/xml

Access URL: https://hal.archives-ouvertes.fr/hal-03295898/document
https://zbmath.org/7212236
https://doi.org/10.1090/mcom/3518
https://www.ams.org/journals/mcom/2020-89-325/S0025-5718-2020-03518-2/home.html
https://dblp.uni-trier.de/db/journals/moc/moc89.html#Flammang20
https://doi.org/10.1090/mcom/3518

The absolute trace of totally positive algebraic integers

Authors: V. Flammang

Contributors: Flammang, Valérie

Source: International Journal of Number Theory. 15:173-181

Subject Terms: recursive algorithm, PV-numbers and generalizations, other special algebraic numbers, Mahler measure, Totally real fields, Algebraic number theory computations, trace, [MATH] Mathematics [math], 0101 mathematics, special algebraic numbers, totally positive algebraic integers, 01 natural sciences, Polynomials in number theory, Trace, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]

File Description: application/pdf; application/xml

Access URL: https://hal.archives-ouvertes.fr/hal-03295884/file/Trace_alpha1_revised3.pdf
https://hal.science/hal-03295884v1
https://hal.science/hal-03295884v1/document
https://doi.org/10.1142/s1793042119500064
https://zbmath.org/7024206
https://doi.org/10.1142/s1793042119500064
https://www.worldscientific.com/doi/10.1142/S1793042119500064

On the smallest houses of reciprocal algebraic integers

Authors: Qiang Wu, Zhuo Zhang

Source: Journal of Number Theory. 177:170-180

Subject Terms: PV-numbers and generalizations, other special algebraic numbers, Mahler measure, integer transfinite diameter, explicit auxiliary function, reciprocal, Algebraic number theory computations, 0101 mathematics, algebraic integer, house, 01 natural sciences, Polynomials in number theory

File Description: application/xml

Access URL: https://zbmath.org/6720633
https://doi.org/10.1016/j.jnt.2017.01.012
https://www.sciencedirect.com/science/article/abs/pii/S0022314X1730077X
https://www.sciencedirect.com/science/article/pii/S0022314X1730077X

The absolute trace of totally positive reciprocal algebraic integers

Authors: Qiang Wu, Xiaoqian Dong

Source: Journal of Number Theory. 170:66-74

Subject Terms: explicit auxiliary function, absolute trace, Algebraic number theory computations, 0101 mathematics, totally positive reciprocal algebraic integers, 01 natural sciences, Algebraic numbers, rings of algebraic integers, Polynomials in number theory

File Description: application/xml

Access URL: https://zbmath.org/6626755
https://doi.org/10.1016/j.jnt.2016.06.016
https://www.sciencedirect.com/science/article/abs/pii/S0022314X16301676
https://www.sciencedirect.com/science/article/pii/S0022314X16301676

RETRACTED: A generalization of the Schur–Siegel–Smyth trace problem: Retracted: A generalization of the Schur-Siegel-Smyth trace problem

Authors: George Shakan, Kyle Pratt, Alexandru Zaharescu

Source: Journal of Mathematical Analysis and Applications. 436:489-500

Subject Terms: minimal polynomial, polynomials with all roots real, Schur-Siegel-Smyth trace problem, totally positive numbers, trace, 0101 mathematics, 01 natural sciences, Algebraic numbers, rings of algebraic integers, Polynomials in number theory

File Description: application/xml

Access URL: https://zbmath.org/6536918
https://doi.org/10.1016/j.jmaa.2015.12.003
https://www.sciencedirect.com/science/article/pii/S0022247X15011099
https://www.sciencedirect.com/science/article/abs/pii/S0022247X15011099
https://experts.illinois.edu/en/publications/a-generalization-of-the-schur-siegel-smyth-trace-problem

The S-measure for algebraic integers having all their conjugates in a sector

Authors: Flammang, Valérie

Contributors: Flammang, Valérie

Source: Rocky Mountain J. Math. 50, no. 6 (2020), 2035-2045
Rocky Mountain J. Math. 50, no. 4 (2020), 1313-1321

Subject Terms: recursive algorithm, algebraic integers, Algebraic number theory computations, measure, [MATH] Mathematics [math], 01 natural sciences, absolute Mahler measure, explicit auxiliary functions, PV-numbers and generalizations, other special algebraic numbers, Mahler measure, 11Y40, 11C08, 11R06, 0101 mathematics, Polynomials in number theory, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]

File Description: application/pdf; application/xml

Access URL: https://hal.archives-ouvertes.fr/hal-03295906/file/Mesure_S.pdf
https://hal.archives-ouvertes.fr/hal-03296091/document
https://hal.science/hal-03295906v1/document
https://hal.science/hal-03295906v1
https://doi.org/10.1216/rmj.2020.50.1313
https://zbmath.org/7261866
https://doi.org/10.1216/rmj.2020.50.1313
http://projecteuclid.org/euclid.rmjm/1601344827
https://projecteuclid.org/journals/rocky-mountain-journal-of-mathematics/volume-50/issue-6/The-N-measure-for-algebraic-integers-having-all-their-conjugates/10.1216/rmj.2020.50.2035.full
https://projecteuclid.org/euclid.rmjm/1609815805
https://projecteuclid.org/euclid.rmjm/1601344827

A Salem number with degree 34 and trace −3: A salem number with degree 34 and trace -3

Authors: El Otmani, S, Rhin, G, Sac-Epee, Jean-Marc

Contributors: Sac-Epee, Jean-Marc

Source: Journal of Number Theory. 150:21-25

Subject Terms: 12D10, Polynomials in real and complex fields: location of zeros (algebraic theorems), 11R09, Polynomials, totally positive algebraic integers, 01 natural sciences, Real polynomials: location of zeros, Mixed integer programming, 11C08, 11S05, 0101 mathematics, 26C10, Polynomials in number theory, Polynomials (irreducibility, etc.), Salem numbers of small trace, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]

File Description: application/pdf; application/xml

Access URL: https://hal.science/hal-01100988v1
https://hal.science/hal-01100988v1/document
https://doi.org/10.1016/j.jnt.2014.11.013
https://hal.archives-ouvertes.fr/hal-01100988/document
https://hal.archives-ouvertes.fr/hal-01100988
https://www.sciencedirect.com/science/article/pii/S0022314X14003886
https://www.sciencedirect.com/science/article/abs/pii/S0022314X14003886

A Lower Bound on the Complexity of Polynomial Multiplication over Finite Fields: A lower bound on the complexity of polynomial multiplication over finite fields

Authors: Michael Kaminski

Source: Lecture Notes in Computer Science ISBN: 9783540249986

Subject Terms: polynomial multiplication, 4. Education, 0102 computer and information sciences, 02 engineering and technology, Symbolic computation and algebraic computation, 01 natural sciences, Polynomials over finite fields, 0202 electrical engineering, electronic engineering, information engineering, Computational aspects of field theory and polynomials, Recurrences, quadratic algorithms, finite fields, Number-theoretic algorithms, complexity, Polynomials in number theory

File Description: application/xml

Access URL: https://zbmath.org/2205880
https://doi.org/10.1137/s0097539704442118
https://link.springer.com/chapter/10.1007/978-3-540-31856-9_40
https://dblp.uni-trier.de/db/conf/stacs/stacs2005.html#Kaminski05
https://rd.springer.com/chapter/10.1007/978-3-540-31856-9_40
https://dblp.uni-trier.de/db/journals/siamcomp/siamcomp34.html#Kaminski05
https://locus.siam.org/doi/abs/10.1137/S0097539704442118
https://epubs.siam.org/doi/abs/10.1137/S0097539704442118
https://doi.org/10.1137/S0097539704442118

Totally positive polynomials with small length

Authors: Flammang, V., Sac-Epee, Jean-Marc

Contributors: Sac-Epee, Jean-Marc

Subject Terms: length of polynomials, Linear programming, auxiliary functions, Polynomials in number theory, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]

File Description: application/pdf; application/xml

Access URL: https://hal.science/hal-02871261v1
https://zbmath.org/7351023

Arithmetic Circuits and Polynomial Replacement Systems: Arithmetic circuits and polynomial replacement systems

Authors: Heribert Vollmer, Klaus W. Wagner, Pierre McKenzie

Source: Lecture Notes in Computer Science ISBN: 9783540414131

Subject Terms: computational complexity, arithmetic circuit, counting classes, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), 0102 computer and information sciences, Models of computation (Turing machines, etc.), 0101 mathematics, 01 natural sciences, Polynomials in number theory

File Description: application/xml

Access URL: https://zbmath.org/2135823
https://doi.org/10.1137/s009753970139207x
https://rd.springer.com/chapter/10.1007/3-540-44450-5_13
https://doi.org/10.1007/3-540-44450-5_13
https://www.thi.uni-hannover.de/fileadmin/forschung/publikationen/daten/mc-vo-wa04.pdf
https://dblp.uni-trier.de/db/conf/fsttcs/fsttcs2000.html#McKenzieVW00
https://link.springer.com/chapter/10.1007/3-540-44450-5_13
https://dl.acm.org/doi/10.1137/S009753970139207X
https://dblp.uni-trier.de/db/journals/siamcomp/siamcomp33.html#McKenzieVW04
https://doi.org/10.1137/S009753970139207X
https://locus.siam.org/doi/abs/10.1137/S009753970139207X
https://epubs.siam.org/doi/10.1137/S009753970139207X

The measure of totally positive algebraic integers

Authors: Quanwu Mu, Qiang Wu

Source: Journal of Number Theory. 133:12-19

Subject Terms: PV-numbers and generalizations, other special algebraic numbers, Mahler measure, Algebra and Number Theory, explicit auxiliary function, LLL algorithm, semi-infinite linear programming, Algebraic number theory computations, 0101 mathematics, 01 natural sciences, totally positive algebraic integer, absolute length, Polynomials in number theory, absolute Mahler measure

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/pii/S0022314X12001989
https://www.sciencedirect.com/science/article/abs/pii/S0022314X12001989

THE TRACE PROBLEM FOR TOTALLY POSITIVE ALGEBRAIC INTEGERS: The trace problem for totally positive algebraic integers

Authors: Yanhua Liang, Qiang Wu

Source: Journal of the Australian Mathematical Society. 90:341-354

Subject Terms: PV-numbers and generalizations, other special algebraic numbers, Mahler measure, Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc, Salem number, explicit auxiliary function, LLL algorithm, absolute trace, semi-infinite linear programming, Algebraic number theory computations, 0101 mathematics, 01 natural sciences, totally positive algebraic integer, Polynomials in number theory

File Description: application/xml

Access URL: https://www.cambridge.org/core/services/aop-cambridge-core/content/view/029C46294DEFED663A0BC6F9320BC674/S1446788711001030a.pdf/div-class-title-the-trace-problem-for-totally-positive-algebraic-integers-div.pdf
https://zbmath.org/5955328
https://doi.org/10.1017/s1446788711001030
https://www.cambridge.org/core/journals/journal-of-the-australian-mathematical-society/article/trace-problem-for-totally-positive-algebraic-integers/029C46294DEFED663A0BC6F9320BC674
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/029C46294DEFED663A0BC6F9320BC674/S1446788711001030a.pdf/div-class-title-the-trace-problem-for-totally-positive-algebraic-integers-div.pdf
https://dialnet.unirioja.es/servlet/articulo?codigo=3739231

The smallest Perron numbers

Authors: Qiang Wu

Source: Mathematics of Computation. 79:2387-2394

Subject Terms: PV-numbers and generalizations, other special algebraic numbers, Mahler measure, transfinite diameter, Algebraic number theory computations, 0101 mathematics, Perron number, algebraic integer, 01 natural sciences, Polynomials in number theory

File Description: application/xml

Access URL: https://www.ams.org/mcom/2010-79-272/S0025-5718-10-02345-8/S0025-5718-10-02345-8.pdf
https://dblp.uni-trier.de/db/journals/moc/moc79.html#Wu10a
https://www.ams.org/mcom/2010-79-272/S0025-5718-10-02345-8/S0025-5718-10-02345-8.pdf
https://www.ams.org/journals/mcom/2010-79-272/S0025-5718-10-02345-8/home.html
https://doi.org/10.1090/S0025-5718-10-02345-8