Class information for:
Level 1: MAHLER MEASURE//SALEM NUMBERS//EXPLICIT AUXILIARY FUNCTION

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
16946 626 15.2 33%


Bar chart of Publication_year

Last years might be incomplete

Hierarchy of classes
The table includes all classes above and classes immediately below the current class.


Cluster id Level Cluster label #P
15 4 MATHEMATICS//MATHEMATICS, APPLIED//MATH 719832
205 3       MATHEMATICS//JOURNAL OF NUMBER THEORY//ACTA ARITHMETICA 52461
3266 2             MAHLER MEASURE//KAC RICE FORMULA//RANDOM ALGEBRAIC POLYNOMIALS 1935
16946 1                   MAHLER MEASURE//SALEM NUMBERS//EXPLICIT AUXILIARY FUNCTION 626

Terms with highest relevance score


rank Term termType Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 MAHLER MEASURE authKW 2032320 12% 56% 75
2 SALEM NUMBERS authKW 758902 4% 68% 23
3 EXPLICIT AUXILIARY FUNCTION authKW 585327 2% 100% 12
4 LEHMERS PROBLEM authKW 462468 3% 59% 16
5 INTEGER TRANSFINITE DIAMETER authKW 395094 1% 90% 9
6 PISOT NUMBERS authKW 374875 4% 27% 28
7 WEIL HEIGHT authKW 334462 2% 57% 12
8 METRIC MAHLER MEASURE authKW 243886 1% 100% 5
9 RESTRICTED COEFFICIENTS authKW 239004 1% 70% 7
10 ALGEBRAIC INTEGER authKW 232401 1% 53% 9

Web of Science journal categories


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 Mathematics 26031 87% 0% 543
2 Mathematics, Applied 1144 18% 0% 112
3 Computer Science, Theory & Methods 19 2% 0% 14
4 Multidisciplinary Sciences 10 1% 0% 6
5 Logic 10 0% 0% 2
6 Computer Science, Cybernetics 0 0% 0% 1
7 Physics, Mathematical 0 1% 0% 6
8 Mathematics, Interdisciplinary Applications -0 0% 0% 2
9 Computer Science, Interdisciplinary Applications -0 0% 0% 3
10 Statistics & Probability -1 0% 0% 2

Address terms


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 UER 48 EQUIPE RECH 294 195109 1% 100% 4
2 CNRSUMR 7122 109747 0% 75% 3
3 UFR MIM 55411 2% 11% 10
4 CNRSUMR 7586UNIV PARIS DIDEROTSORBONNE PARIS C 48777 0% 100% 1
5 EQUIPE RECH 294 UER 48 48777 0% 100% 1
6 IECLUFR MIM 48777 0% 100% 1
7 IECLUMR CNRS 7502CS 50128 48777 0% 100% 1
8 INFORMAT PARALLEELISME 48777 0% 100% 1
9 MATH PHYS COMP ELE NUMBER THEORY 48777 0% 100% 1
10 MATH SATIST 48777 0% 100% 1

Journals


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 ACTA ARITHMETICA 66062 11% 2% 66
2 JOURNAL OF NUMBER THEORY 32526 9% 1% 56
3 MATHEMATICS OF COMPUTATION 19629 6% 1% 40
4 RAMANUJAN JOURNAL 13653 3% 2% 17
5 EXPERIMENTAL MATHEMATICS 11329 2% 2% 13
6 JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX 8232 1% 3% 6
7 CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES 6087 3% 1% 17
8 COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A 5616 1% 2% 6
9 INTERNATIONAL JOURNAL OF NUMBER THEORY 3510 1% 1% 9
10 COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE 3285 4% 0% 24

Author Key Words


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class		 LCSH search Wikipedia search
1 MAHLER MEASURE 2032320 12% 56% 75 Search MAHLER+MEASURE Search MAHLER+MEASURE
2 SALEM NUMBERS 758902 4% 68% 23 Search SALEM+NUMBERS Search SALEM+NUMBERS
3 EXPLICIT AUXILIARY FUNCTION 585327 2% 100% 12 Search EXPLICIT+AUXILIARY+FUNCTION Search EXPLICIT+AUXILIARY+FUNCTION
4 LEHMERS PROBLEM 462468 3% 59% 16 Search LEHMERS+PROBLEM Search LEHMERS+PROBLEM
5 INTEGER TRANSFINITE DIAMETER 395094 1% 90% 9 Search INTEGER+TRANSFINITE+DIAMETER Search INTEGER+TRANSFINITE+DIAMETER
6 PISOT NUMBERS 374875 4% 27% 28 Search PISOT+NUMBERS Search PISOT+NUMBERS
7 WEIL HEIGHT 334462 2% 57% 12 Search WEIL+HEIGHT Search WEIL+HEIGHT
8 METRIC MAHLER MEASURE 243886 1% 100% 5 Search METRIC+MAHLER+MEASURE Search METRIC+MAHLER+MEASURE
9 RESTRICTED COEFFICIENTS 239004 1% 70% 7 Search RESTRICTED+COEFFICIENTS Search RESTRICTED+COEFFICIENTS
10 ALGEBRAIC INTEGER 232401 1% 53% 9 Search ALGEBRAIC+INTEGER Search ALGEBRAIC+INTEGER

Core articles
The table includes core articles in the class. The following variables is taken into account for the relevance score of an article in a cluster c:
(1) Number of references referring to publications in the class.
(2) Share of total number of active references referring to publications in the class.
(3) Age of the article. New articles get higher score than old articles.
(4) Citation rate, normalized to year.


Rank Reference # ref.
in cl.		 Shr. of ref. in
cl.		 Citations
1 SMYTH, C , (2015) SEVENTY YEARS OF SALEM NUMBERS.BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. VOL. 47. ISSUE . P. 379 -395 47 78% 4
2 ERDELYI, T , (2016) COPPERSMITH-RIVLIN TYPE INEQUALITIES AND THE ORDER OF VANISHING OF POLYNOMIALS AT 1.ACTA ARITHMETICA. VOL. 172. ISSUE 3. P. 271 -284 20 71% 0
3 ERDELYI, T , (2016) THE NUMBER OF UNIMODULAR ZEROS OF SELF-RECIPROCAL POLYNOMIALS WITH COEFFICIENTS IN A FINITE SET.ACTA ARITHMETICA. VOL. 176. ISSUE 2. P. 177 -200 22 65% 0
4 MOSSINGHOFF, MJ , RHIN, G , WU, Q , (2008) MINIMAL MAHLER MEASURES.EXPERIMENTAL MATHEMATICS. VOL. 17. ISSUE 4. P. 451 -458 17 89% 7
5 ERDELYI, T , (2015) PSEUDO-BOOLEAN FUNCTIONS AND THE MULTIPLICITY OF THE ZEROS OF POLYNOMIALS.JOURNAL D ANALYSE MATHEMATIQUE. VOL. 127. ISSUE . P. 91 -108 17 74% 0
6 MU, QW , WU, Q , (2013) THE MEASURE OF TOTALLY POSITIVE ALGEBRAIC INTEGERS.JOURNAL OF NUMBER THEORY. VOL. 133. ISSUE 1. P. 12 -19 12 100% 3
7 MCKEE, J , YATSYNA, P , (2016) SALEM NUMBERS OF TRACE-2, AND A CONJECTURE OF ESTES AND GURALNICK.JOURNAL OF NUMBER THEORY. VOL. 160. ISSUE . P. 409 -417 13 87% 0
8 GHATE, E , HIRONAKA, E , (2001) THE ARITHMETIC AND GEOMETRY OF SALEM NUMBERS.BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY. VOL. 38. ISSUE 3. P. 293 -314 16 94% 18
9 DUBICKAS, A , (2009) ON THE FRACTIONAL PARTS OF RATIONAL POWERS.INTERNATIONAL JOURNAL OF NUMBER THEORY. VOL. 5. ISSUE 6. P. 1037 -1048 12 100% 2
10 DUBICKAS, A , (2009) AN APPROXIMATION PROPERTY OF LACUNARY SEQUENCES.ISRAEL JOURNAL OF MATHEMATICS. VOL. 170. ISSUE 1. P. 95 -111 12 100% 1

Classes with closest relation at Level 1


Rank Class id link
1 29164 MERIT FACTOR//LITTLEWOOD POLYNOMIALS//FEKETE POLYNOMIALS
2 32718 LINEAR POLARIZATION CONSTANTS//POLARIZATION CONSTANT//PRODUCT OF LINEAR FUNCTIONALS
3 36324 NATURAL SPECTRUM//F M RIESZ THEOREM//SPECTRUM OF MEASURE
4 4357 ARITHMETIC DYNAMICS//ANDRE OORT CONJECTURE//ACTA ARITHMETICA
5 24058 ALGEBRAIC ENTROPY//ALGEBRAIC ACTION//MEAN DIMENSION
6 30095 3X1 PROBLEM//COLLATZ PROBLEM//3X1 CONJECTURE
7 25091 LPTHIRM//IAESB//WHEATSTONE PHYS
8 28866 NOWHERE DIFFERENTIABLE FUNCTION//SINGULAR FUNCTIONS//TAKAGIS FUNCTION
9 37400 BEURLING GENERALIZED PRIMES//BEURLING GENERALIZED NUMBERS//CHEBYSHEV PRIME BOUNDS
10 29968 SCATTERED SUBWORD//PARIKH MATRIX//SUBWORD

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