Class information for:
Level 1: L FUNCTIONS//AUTOMORPHIC L FUNCTIONS//SELBERG CLASS

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
5000 1690 19.0 37%


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
1206 2             ACTA ARITHMETICA//JOURNAL OF NUMBER THEORY//MATHEMATICS 9179
5000 1                   L FUNCTIONS//AUTOMORPHIC L FUNCTIONS//SELBERG CLASS 1690

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 L FUNCTIONS authKW 522740 6% 27% 108
2 AUTOMORPHIC L FUNCTIONS authKW 466640 2% 70% 37
3 SELBERG CLASS authKW 454002 2% 74% 34
4 RANKIN SELBERG L FUNCTION authKW 387357 2% 79% 27
5 RIEMANN ZETA FUNCTION authKW 375747 6% 20% 106
6 SYMMETRIC SQUARE L FUNCTION authKW 301514 1% 76% 22
7 MAASS FORMS authKW 283259 2% 56% 28
8 SUBCONVEXITY authKW 274798 1% 89% 17
9 LOW LYING ZEROS authKW 270998 1% 100% 15
10 CUSP FORMS authKW 266028 2% 41% 36

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 84863 95% 0% 1608
2 Mathematics, Applied 1754 14% 0% 234
3 Physics, Mathematical 72 3% 0% 43
4 COMPUTER APPLICATIONS & CYBERNETICS 5 0% 0% 1
5 Statistics & Probability 0 1% 0% 10
6 Multidisciplinary Sciences -3 0% 0% 1
7 Computer Science, Software Engineering -4 0% 0% 3
8 Thermodynamics -9 0% 0% 1
9 Computer Science, Theory & Methods -10 0% 0% 1
10 Energy & Fuels -15 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 MODERN MATH 90333 0% 100% 5
2 D MATH 39019 1% 20% 11
3 MATH 37870 56% 0% 938
4 TAN 24087 0% 67% 2
5 RAYMOND BEVERLY SACKLER MATH SCI 19620 1% 11% 10
6 ALGORITHMIQUE ARITHMET 18067 0% 100% 1
7 ANAL THEORY 18067 0% 100% 1
8 AQUIPE ARITHMET GEOMETRIE ALGEBR 18067 0% 100% 1
9 EQUIPE ARITHMET GEOMETRIE ALGEB 18067 0% 100% 1
10 HENRY KOERNER EMERITUS 18067 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 128041 9% 5% 151
2 JOURNAL OF NUMBER THEORY 125933 11% 4% 181
3 INTERNATIONAL JOURNAL OF NUMBER THEORY 41859 3% 5% 51
4 INTERNATIONAL MATHEMATICS RESEARCH NOTICES 29530 4% 2% 70
5 PROGRESS IN MATHEMATICS 18065 0% 50% 2
6 DUKE MATHEMATICAL JOURNAL 17973 3% 2% 54
7 RAMANUJAN JOURNAL 16796 2% 3% 31
8 PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES 14082 2% 2% 42
9 MATHEMATIKA 12990 1% 3% 25
10 FORUM MATHEMATICUM 12734 2% 2% 30

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 L FUNCTIONS 522740 6% 27% 108 Search L+FUNCTIONS Search L+FUNCTIONS
2 AUTOMORPHIC L FUNCTIONS 466640 2% 70% 37 Search AUTOMORPHIC+L+FUNCTIONS Search AUTOMORPHIC+L+FUNCTIONS
3 SELBERG CLASS 454002 2% 74% 34 Search SELBERG+CLASS Search SELBERG+CLASS
4 RANKIN SELBERG L FUNCTION 387357 2% 79% 27 Search RANKIN+SELBERG+L+FUNCTION Search RANKIN+SELBERG+L+FUNCTION
5 RIEMANN ZETA FUNCTION 375747 6% 20% 106 Search RIEMANN+ZETA+FUNCTION Search RIEMANN+ZETA+FUNCTION
6 SYMMETRIC SQUARE L FUNCTION 301514 1% 76% 22 Search SYMMETRIC+SQUARE+L+FUNCTION Search SYMMETRIC+SQUARE+L+FUNCTION
7 MAASS FORMS 283259 2% 56% 28 Search MAASS+FORMS Search MAASS+FORMS
8 SUBCONVEXITY 274798 1% 89% 17 Search SUBCONVEXITY Search SUBCONVEXITY
9 LOW LYING ZEROS 270998 1% 100% 15 Search LOW+LYING+ZEROS Search LOW+LYING+ZEROS
10 CUSP FORMS 266028 2% 41% 36 Search CUSP+FORMS Search CUSP+FORMS

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 FIORILLI, D , MILLER, SJ , (2015) SURPASSING THE RATIOS CONJECTURE IN THE 1-LEVEL DENSITY OF DIRICHLET L-FUNCTIONS.ALGEBRA & NUMBER THEORY. VOL. 9. ISSUE 1. P. 13 -52 34 87% 2
2 MILINOVICH, MB , NG, N , (2014) SIMPLE ZEROS OF MODULAR L-FUNCTIONS.PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY. VOL. 109. ISSUE . P. 1465 -1506 32 94% 3
3 BARRETT, O , MCDONALD, B , MILLER, SJ , RYAN, P , TURNAGE-BUTTERBAUGH, CL , WINSOR, K , (2015) GAPS BETWEEN ZEROS OF GL(2) L-FUNCTIONS.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. VOL. 429. ISSUE 1. P. 204 -232 31 97% 0
4 DUENEZ, E , HUYNH, DK , KEATING, JP , MILLER, SJ , SNAITH, NC , (2012) A RANDOM MATRIX MODEL FOR ELLIPTIC CURVE L-FUNCTIONS OF FINITE CONDUCTOR.JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. VOL. 45. ISSUE 11. P. - 36 82% 4
5 BLOMER, V , MILICEVIC, D , (2015) THE SECOND MOMENT OF TWISTED MODULAR L-FUNCTIONS.GEOMETRIC AND FUNCTIONAL ANALYSIS. VOL. 25. ISSUE 2. P. 453 -516 28 88% 3
6 MASON, AM , SNAITH, NC , (2016) SYMPLECTIC N-LEVEL DENSITIES WITH RESTRICTED SUPPORT.RANDOM MATRICES-THEORY AND APPLICATIONS. VOL. 5. ISSUE 4. P. - 25 100% 0
7 ANDRADE, JC , KEATING, JP , (2014) CONJECTURES FOR THE INTEGRAL MOMENTS AND RATIOS OF L-FUNCTIONS OVER FUNCTION FIELDS.JOURNAL OF NUMBER THEORY. VOL. 142. ISSUE . P. 102-148 25 96% 4
8 SNAITH, NC , (2010) RIEMANN ZEROS AND RANDOM MATRIX THEORY.MILAN JOURNAL OF MATHEMATICS. VOL. 78. ISSUE 1. P. 135-152 33 80% 6
9 MILLER, SJ , MONTAGUE, D , (2011) AN ORTHOGONAL TEST OF THE L-FUNCTIONS RATIOS CONJECTURE, II.ACTA ARITHMETICA. VOL. 146. ISSUE 1. P. 53-90 26 100% 2
10 MILINOVICH, MB , TURNAGE-BUTTERBAUGH, CL , (2014) MOMENTS OF PRODUCTS OF AUTOMORPHIC L-FUNCTIONS.JOURNAL OF NUMBER THEORY. VOL. 139. ISSUE . P. 175-204 27 84% 5

Classes with closest relation at Level 1


Rank Class id link
1 25860 ESTERMANN ZETA FUNCTION//RIEMANN HYPOTHESIS//COTANGENT SUMS
2 29343 SPACE OF ANALYTIC FUNCTIONS//JOINT UNIVERSALITY//PERIODIC HURWITZ ZETA FUNCTION
3 13255 DIRICHLET DIVISOR PROBLEM//DIVISOR PROBLEM//LATTICE POINTS
4 19793 PRIMES IN RESIDUE CLASSES//CHEBYSHEVS BIAS//FACTORIZATIONS OF DISTINCT LENGTHS
5 22454 MULTIPLE SINE FUNCTION//MULTIPLE GAMMA FUNCTION//SELBERG ZETA FUNCTION
6 14027 CIRCLE METHOD//WARING GOLDBACH PROBLEM//SIEVE METHODS
7 14256 QUANTUM ERGODICITY//DCAIN//EIGENFUNCTION ESTIMATES
8 7742 SIEGEL MODULAR FORMS//JACOBI FORMS//ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG
9 30279 WHITTAKER FUNCTIONS//WHITTAKER MODELS//GENERALIZED WHITTAKER MODEL
10 1219 DISTINGUISHED REPRESENTATIONS//AUTOMORPHIC REPRESENTATIONS//ORBITAL INTEGRALS

Go to start page