Class information for:
Level 2: MAHLER MEASURE//KAC RICE FORMULA//RANDOM ALGEBRAIC POLYNOMIALS

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
3266 1935 14.8 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
14479 1                   MAHLERS METHOD//IRRATIONALITY MEASURE//ALGEBRAIC INDEPENDENCE 767
16946 1                   MAHLER MEASURE//SALEM NUMBERS//EXPLICIT AUXILIARY FUNCTION 626
24654 1                   KAC RICE FORMULA//RANDOM ALGEBRAIC POLYNOMIALS//RANDOM POLYNOMIALS 305
32718 1                   LINEAR POLARIZATION CONSTANTS//POLARIZATION CONSTANT//PRODUCT OF LINEAR FUNCTIONALS 135
35085 1                   INTEGER VALUED ENTIRE FUNCTION//RECURRENT STEP EQUATIONS//ABEL ARITHMETIC FUNCTIONS 102

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 711032 4% 58% 78
2 KAC RICE FORMULA authKW 426569 1% 97% 28
3 RANDOM ALGEBRAIC POLYNOMIALS authKW 395052 1% 96% 26
4 RANDOM POLYNOMIALS authKW 376096 2% 57% 42
5 MAHLERS METHOD authKW 299797 1% 100% 19
6 NUMBER OF REAL ZEROS authKW 286883 1% 91% 20
7 IRRATIONALITY MEASURE authKW 282841 1% 81% 22
8 SALEM NUMBERS authKW 245485 1% 68% 23
9 ALGEBRAIC INDEPENDENCE authKW 213534 2% 44% 31
10 IRRATIONALITY authKW 197180 2% 31% 40

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 78186 86% 0% 1655
2 Mathematics, Applied 3621 18% 0% 350
3 Statistics & Probability 438 4% 0% 81
4 Physics, Mathematical 97 3% 0% 52
5 Computer Science, Theory & Methods 44 2% 0% 39
6 Multidisciplinary Sciences 25 1% 0% 17
7 Logic 5 0% 0% 3
8 Mechanics 5 2% 0% 32
9 Computer Science, Cybernetics -0 0% 0% 1
10 Education, Scientific Disciplines -3 0% 0% 1

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 HH WIRT AFT 78894 0% 100% 5
2 UER 48 EQUIPE RECH 294 63115 0% 100% 4
3 PLICAT FUZZY MODELING 49353 1% 13% 24
4 UO 39927 0% 28% 9
5 CNRSUMR 7122 35501 0% 75% 3
6 CNRS FRE 2271 31558 0% 100% 2
7 MATEMAATTISTEN TIETEIDEN LAITOS 31558 0% 100% 2
8 UFR MIM 30280 1% 15% 13
9 EQUIPE ARITHMET GEOMETRIE ALGEBR 22946 0% 36% 4
10 MATH 17576 36% 0% 693

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 125533 8% 5% 160
2 JOURNAL OF NUMBER THEORY 65712 7% 3% 140
3 RAMANUJAN JOURNAL 22048 2% 4% 38
4 INTERNATIONAL JOURNAL OF NUMBER THEORY 19215 2% 3% 37
5 VESTNIK MOSKOVSKOGO UNIVERSITETA SERIYA 1 MATEMATIKA MEKHANIKA 11921 1% 3% 28
6 MATHEMATICAL NOTES 11698 3% 1% 61
7 MATHEMATICS OF COMPUTATION 9470 3% 1% 49
8 JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX 8943 1% 5% 11
9 EXPERIMENTAL MATHEMATICS 6248 1% 2% 17
10 COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE 5153 3% 1% 53

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 711032 4% 58% 78 Search MAHLER+MEASURE Search MAHLER+MEASURE
2 KAC RICE FORMULA 426569 1% 97% 28 Search KAC+RICE+FORMULA Search KAC+RICE+FORMULA
3 RANDOM ALGEBRAIC POLYNOMIALS 395052 1% 96% 26 Search RANDOM+ALGEBRAIC+POLYNOMIALS Search RANDOM+ALGEBRAIC+POLYNOMIALS
4 RANDOM POLYNOMIALS 376096 2% 57% 42 Search RANDOM+POLYNOMIALS Search RANDOM+POLYNOMIALS
5 MAHLERS METHOD 299797 1% 100% 19 Search MAHLERS+METHOD Search MAHLERS+METHOD
6 NUMBER OF REAL ZEROS 286883 1% 91% 20 Search NUMBER+OF+REAL+ZEROS Search NUMBER+OF+REAL+ZEROS
7 IRRATIONALITY MEASURE 282841 1% 81% 22 Search IRRATIONALITY+MEASURE Search IRRATIONALITY+MEASURE
8 SALEM NUMBERS 245485 1% 68% 23 Search SALEM+NUMBERS Search SALEM+NUMBERS
9 ALGEBRAIC INDEPENDENCE 213534 2% 44% 31 Search ALGEBRAIC+INDEPENDENCE Search ALGEBRAIC+INDEPENDENCE
10 IRRATIONALITY 197180 2% 31% 40 Search IRRATIONALITY Search IRRATIONALITY

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 ZUDILIN, W , (2011) ARITHMETIC HYPERGEOMETRIC SERIES.RUSSIAN MATHEMATICAL SURVEYS. VOL. 66. ISSUE 2. P. 369 -420 43 54% 5
3 PINASCO, D , (2012) LOWER BOUNDS FOR NORMS OF PRODUCTS OF POLYNOMIALS VIA BOMBIERI INEQUALITY.TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. VOL. 364. ISSUE 8. P. 3993 -4010 24 83% 3
4 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 25 74% 0
5 BLEHER, P , HOMMA, Y , ROEDER, RKW , (2016) TWO-POINT CORRELATION FUNCTIONS AND UNIVERSALITY FOR THE ZEROS OF SYSTEMS OF SO(N+1)-INVARIANT GAUSSIAN RANDOM POLYNOMIALS.INTERNATIONAL MATHEMATICS RESEARCH NOTICES. VOL. . ISSUE 11. P. 3237 -3278 16 100% 0
6 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
7 NATHANSON, MB , (2017) FREE MONOIDS AND FORESTS OF RATIONAL NUMBERS.DISCRETE APPLIED MATHEMATICS. VOL. 216. ISSUE . P. 662 -669 8 100% 1
8 VAN ASSCHE, W , (2010) HERMITE-PADE RATIONAL APPROXIMATION TO IRRATIONAL NUMBERS.COMPUTATIONAL METHODS AND FUNCTION THEORY. VOL. 10. ISSUE 2. P. 585-602 15 100% 0
9 FISCHLER, S , RIVOAL, T , (2016) MULTIPLE ZETA VALUES, PADE APPROXIMATION AND VASILYEV'S CONJECTURE.ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE. VOL. 15. ISSUE . P. 1 -24 13 100% 0
10 MOSSINGHOFF, MJ , RHIN, G , WU, Q , (2008) MINIMAL MAHLER MEASURES.EXPERIMENTAL MATHEMATICS. VOL. 17. ISSUE 4. P. 451 -458 17 89% 7

Classes with closest relation at Level 2


Rank Class id link
1 1098 HAUSDORFF DIMENSION//ERGODIC THEORY AND DYNAMICAL SYSTEMS//MATHEMATICS
2 376 JOURNAL OF NUMBER THEORY//MATHEMATICS//ACTA ARITHMETICA
3 1244 FIBONACCI QUARTERLY//MULTIPLE ZETA VALUES//BERNOULLI NUMBERS
4 1909 MODULAR FORMS//RAMANUJAN JOURNAL//THETA FUNCTIONS
5 2388 RANDOM MATRICES//RANDOM MATRICES-THEORY AND APPLICATIONS//RANDOM MATRIX
6 3826 QUADRATIC STOCHASTIC OPERATOR//GREATEST TYPE DIVISOR//EVOLUTION ALGEBRA
7 1193 ORTHOGONAL POLYNOMIALS//JOURNAL OF APPROXIMATION THEORY//JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
8 3326 DELAFOSSITE//CUALO2//CUFEO2
9 1206 ACTA ARITHMETICA//JOURNAL OF NUMBER THEORY//MATHEMATICS
10 2945 MEROMORPHIC FUNCTION//NEVANLINNA THEORY//NORMAL FAMILY

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