Class information for:
Level 1: THETA FUNCTIONS//MODULAR EQUATIONS//CONVOLUTION SUMS

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
13453 835 16.0 31%


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
1909 2             MODULAR FORMS//RAMANUJAN JOURNAL//THETA FUNCTIONS 5891
13453 1                   THETA FUNCTIONS//MODULAR EQUATIONS//CONVOLUTION SUMS 835

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 THETA FUNCTIONS authKW 1649447 16% 33% 135
2 MODULAR EQUATIONS authKW 1364677 7% 60% 62
3 CONVOLUTION SUMS authKW 992047 3% 94% 29
4 EISENSTEIN SERIES authKW 879716 10% 30% 80
5 DEDEKIND ETA FUNCTION authKW 658197 4% 60% 30
6 ROGERS RAMANUJAN FUNCTIONS authKW 585086 2% 100% 16
7 ROGERS RAMANUJAN CONTINUED FRACTION authKW 440328 2% 71% 17
8 CIRCULAR SUMMATION authKW 402246 1% 100% 11
9 LAMBERT SERIES authKW 343092 3% 45% 21
10 RAMANUJAN JOURNAL journal 340791 12% 10% 98

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 36878 89% 0% 746
2 Mathematics, Applied 2449 22% 0% 186
3 Physics, Mathematical 45 3% 0% 23
4 Statistics & Probability 4 1% 0% 9
5 Asian Studies 1 0% 0% 1
6 Mathematics, Interdisciplinary Applications 0 1% 0% 5
7 History & Philosophy of Science 0 0% 0% 1
8 Humanities, Multidisciplinary -0 0% 0% 1
9 Planning & Development -0 0% 0% 1
10 Computer Science, Software Engineering -0 0% 0% 3

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 ALGEBRA NUMBER THEORY 126991 4% 10% 36
2 NORTH SHORE MAIL 67023 1% 17% 11
3 STUDIES MATH 54273 2% 11% 14
4 N SHORE MAIL 45938 2% 8% 15
5 INFORMAT MATH SCI 44304 3% 4% 27
6 COMP ASSISTED MATH ITS PLICAT CARMA 38084 1% 21% 5
7 COMP ASSISTED MATH 36568 0% 100% 1
8 EDUC ZABID 36568 0% 100% 1
9 FYS NEXM 36568 0% 100% 1
10 HBEREICH MATH 08 36568 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 RAMANUJAN JOURNAL 340791 12% 10% 98
2 INTERNATIONAL JOURNAL OF NUMBER THEORY 159853 8% 6% 70
3 JOURNAL OF NUMBER THEORY 30842 8% 1% 63
4 ACTA ARITHMETICA 30701 6% 2% 52
5 AMERICAN MATHEMATICAL MONTHLY 14700 4% 1% 33
6 MATHEMATICAL INTELLIGENCER 11878 2% 2% 14
7 EXPERIMENTAL MATHEMATICS 9845 2% 2% 14
8 ROCKY MOUNTAIN JOURNAL OF MATHEMATICS 6418 3% 1% 23
9 INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS 3529 1% 1% 11
10 JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 3311 5% 0% 44

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 THETA FUNCTIONS 1649447 16% 33% 135 Search THETA+FUNCTIONS Search THETA+FUNCTIONS
2 MODULAR EQUATIONS 1364677 7% 60% 62 Search MODULAR+EQUATIONS Search MODULAR+EQUATIONS
3 CONVOLUTION SUMS 992047 3% 94% 29 Search CONVOLUTION+SUMS Search CONVOLUTION+SUMS
4 EISENSTEIN SERIES 879716 10% 30% 80 Search EISENSTEIN+SERIES Search EISENSTEIN+SERIES
5 DEDEKIND ETA FUNCTION 658197 4% 60% 30 Search DEDEKIND+ETA+FUNCTION Search DEDEKIND+ETA+FUNCTION
6 ROGERS RAMANUJAN FUNCTIONS 585086 2% 100% 16 Search ROGERS+RAMANUJAN+FUNCTIONS Search ROGERS+RAMANUJAN+FUNCTIONS
7 ROGERS RAMANUJAN CONTINUED FRACTION 440328 2% 71% 17 Search ROGERS+RAMANUJAN+CONTINUED+FRACTION Search ROGERS+RAMANUJAN+CONTINUED+FRACTION
8 CIRCULAR SUMMATION 402246 1% 100% 11 Search CIRCULAR+SUMMATION Search CIRCULAR+SUMMATION
9 LAMBERT SERIES 343092 3% 45% 21 Search LAMBERT+SERIES Search LAMBERT+SERIES
10 DIVISOR FUNCTIONS 325776 2% 64% 14 Search DIVISOR+FUNCTIONS Search DIVISOR+FUNCTIONS

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 LIU, ZG , (2012) SOME INVERSE RELATIONS AND THETA FUNCTION IDENTITIES.INTERNATIONAL JOURNAL OF NUMBER THEORY. VOL. 8. ISSUE 8. P. 1977-2002 21 100% 7
2 CHAN, HH , COOPER, S , (2012) RATIONAL ANALOGUES OF RAMANUJAN'S SERIES FOR 1/PI.MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY. VOL. 153. ISSUE . P. 361 -383 22 96% 6
3 MA, XR , WEI, RZ , (2017) THE T-COEFFICIENT METHOD III: A GENERAL SERIES EXPANSION FOR THE PRODUCT OF THETA FUNCTIONS WITH DIFFERENT BASES AND ITS APPLICATIONS.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. VOL. 449. ISSUE 1. P. 244 -264 20 95% 0
4 LIU, ZG , (2012) A SUMMATION FORMULA AND RAMANUJAN TYPE SERIES.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. VOL. 389. ISSUE 2. P. 1059 -1065 20 100% 6
5 LIU, XF , LUO, QM , (2015) A NOTE FOR ALTERNATING RAMANUJAN'S CIRCULAR SUMMATION FORMULA.FORUM MATHEMATICUM. VOL. 27. ISSUE 6. P. 3189 -3203 19 100% 0
6 WEI, CA , GONG, DX , (2013) EXTENSIONS OF RAMANUJAN'S TWO FORMULAS FOR 1/PI.JOURNAL OF NUMBER THEORY. VOL. 133. ISSUE 7. P. 2206-2216 22 88% 1
7 ZHOU, Y , LUO, QM , (2014) CIRCULAR SUMMATION FORMULAS FOR THETA FUNCTION NU(4)(Z VERTICAL BAR TAU).ADVANCES IN DIFFERENCE EQUATIONS. VOL. . ISSUE . P. - 19 100% 0
8 ALACA, S , KESICIOGLU, Y , (2016) EVALUATION OF THE CONVOLUTION SUMS SIGMA(L+27M=N) SIGMA(L)SIGMA(M) AND SIGMA(L+32M=N) SIGMA(L)SIGMA(M).INTERNATIONAL JOURNAL OF NUMBER THEORY. VOL. 12. ISSUE 1. P. 1 -13 16 100% 1
9 BARUAH, ND , BERNDT, BC , CHAN, HH , (2009) RAMANUJAN'S SERIES FOR 1/PI: A SURVEY.AMERICAN MATHEMATICAL MONTHLY. VOL. 116. ISSUE 7. P. 567-587 20 91% 31
10 MA, XR , (2014) THE T-COEFFICIENT METHOD II: A NEW SERIES EXPANSION FORMULA OF THETA FUNCTION PRODUCTS AND ITS IMPLICATIONS.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. VOL. 411. ISSUE 2. P. 902-915 17 94% 0

Classes with closest relation at Level 1


Rank Class id link
1 6714 OVERPARTITIONS//PARTITIONS//ROGERS RAMANUJAN IDENTITIES
2 15354 WEAKLY HOLOMORPHIC MODULAR FORMS//GENERALIZED MODULAR FORMS//BORCHERDS PRODUCT
3 33651 NORMAL NUMBERS//CANTOR SERIES//POLYNOMIAL TIME RANDOMNESS
4 22321 SPINOR CLASS FIELDS//TERNARY QUADRATIC FORMS//REPRESENTATIONS OF INTEGERS
5 14479 MAHLERS METHOD//IRRATIONALITY MEASURE//ALGEBRAIC INDEPENDENCE
6 25091 LPTHIRM//IAESB//WHEATSTONE PHYS
7 14579 SUPERCONGRUENCES//GAUSSIAN HYPERGEOMETRIC SERIES//BINOMIAL COEFFICIENTS
8 16946 MAHLER MEASURE//SALEM NUMBERS//EXPLICIT AUXILIARY FUNCTION
9 11098 SEIFFERT MEAN//LOGARITHMIC MEAN//POWER MEAN
10 9297 BASIC HYPERGEOMETRIC SERIES//ABELS LEMMA ON SUMMATION BY PARTS//Q SERIES

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