메뉴 건너뛰기




Volumn 208, Issue 2, 2007, Pages 935-961

Sums of triangular numbers from the Frobenius determinant

Author keywords

Affine superalgebra; Denominator formula; Frobenius determinant; Pfaffian; Sums of triangular numbers

Indexed keywords


EID: 33750627763     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2006.04.006     Document Type: Article
Times cited : (17)

References (20)
  • 1
    • 0039326195 scopus 로고
    • Hypergeometric and modular function identities, and new rational approximations to and continued fraction expansions of classical constants and functions
    • A Tribute to Emil Grosswald: Number Theory and Related Analysis, Amer. Math. Soc., Providence, RI
    • Chudnovsky D.V., and Chudnovsky G.V. Hypergeometric and modular function identities, and new rational approximations to and continued fraction expansions of classical constants and functions. A Tribute to Emil Grosswald: Number Theory and Related Analysis. Contemp. Math. vol. 143 (1993), Amer. Math. Soc., Providence, RI 117-162
    • (1993) Contemp. Math. , vol.143 , pp. 117-162
    • Chudnovsky, D.V.1    Chudnovsky, G.V.2
  • 3
    • 0003351912 scopus 로고
    • Theta Functions on Riemann Surfaces
    • Springer, Berlin
    • Fay J.D. Theta Functions on Riemann Surfaces. Lecture Notes in Math. vol. 352 (1973), Springer, Berlin
    • (1973) Lecture Notes in Math. , vol.352
    • Fay, J.D.1
  • 4
    • 0038950958 scopus 로고
    • Schottky relations on frac(1, 2) (C - C)
    • Theta Functions-Bowdoin 1987, Part 1, Amer. Math. Soc., Providence, RI
    • Fay J. Schottky relations on frac(1, 2) (C - C). Theta Functions-Bowdoin 1987, Part 1. Proc. Sympos. Pure Math. vol. 49 (1989), Amer. Math. Soc., Providence, RI 485-502
    • (1989) Proc. Sympos. Pure Math. , vol.49 , pp. 485-502
    • Fay, J.1
  • 5
    • 84941501618 scopus 로고
    • Über die elliptischen Functionen zweiter Art
    • Frobenius F.G. Über die elliptischen Functionen zweiter Art. J. Reine Angew. Math. 93 (1882) 53-68
    • (1882) J. Reine Angew. Math. , vol.93 , pp. 53-68
    • Frobenius, F.G.1
  • 8
    • 0036800452 scopus 로고    scopus 로고
    • Partition identities and a theorem of Zagier
    • Getz J., and Mahlburg K. Partition identities and a theorem of Zagier. J. Combin. Theory Ser. A 100 (2002) 27-43
    • (2002) J. Combin. Theory Ser. A , vol.100 , pp. 27-43
    • Getz, J.1    Mahlburg, K.2
  • 9
    • 49449126179 scopus 로고
    • Lie superalgebras
    • Kac V.G. Lie superalgebras. Adv. Math. 26 (1977) 8-96
    • (1977) Adv. Math. , vol.26 , pp. 8-96
    • Kac, V.G.1
  • 10
    • 0000192792 scopus 로고
    • Integrable highest weight modules over affine superalgebras and number theory
    • Lie Theory and Geometry, Birkhäuser, Boston, MA
    • Kac V.G., and Wakimoto M. Integrable highest weight modules over affine superalgebras and number theory. Lie Theory and Geometry. Progr. Math. vol. 123 (1994), Birkhäuser, Boston, MA 415-456
    • (1994) Progr. Math. , vol.123 , pp. 415-456
    • Kac, V.G.1    Wakimoto, M.2
  • 11
    • 1042279873 scopus 로고    scopus 로고
    • Multiple elliptic hypergeometric series. An approach from the Cauchy determinant
    • Kajihara Y., and Noumi M. Multiple elliptic hypergeometric series. An approach from the Cauchy determinant. Indag. Math. 14 (2003) 395-421
    • (2003) Indag. Math. , vol.14 , pp. 395-421
    • Kajihara, Y.1    Noumi, M.2
  • 12
    • 27644456268 scopus 로고    scopus 로고
    • Advanced determinant calculus: A complement
    • Krattenthaler C. Advanced determinant calculus: A complement. Linear Algebra Appl. 411 (2005) 68-166
    • (2005) Linear Algebra Appl. , vol.411 , pp. 68-166
    • Krattenthaler, C.1
  • 13
    • 0030467984 scopus 로고    scopus 로고
    • New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan's tau function
    • Milne S.C. New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan's tau function. Proc. Natl. Acad. Sci. USA 93 (1996) 15004-15008
    • (1996) Proc. Natl. Acad. Sci. USA , vol.93 , pp. 15004-15008
    • Milne, S.C.1
  • 14
    • 0036285878 scopus 로고    scopus 로고
    • Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions
    • Milne S.C. Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions. Ramanujan J. 6 (2002) 7-149
    • (2002) Ramanujan J. , vol.6 , pp. 7-149
    • Milne, S.C.1
  • 15
    • 33750611186 scopus 로고    scopus 로고
    • S. Okada, An elliptic generalization of Schur's Pfaffian identity, Adv. Math., in press
  • 16
    • 33750616917 scopus 로고    scopus 로고
    • Recurrences for elliptic hypergeometric integrals
    • Elliptic Integrable Systems, Kobe University
    • Rains E.M. Recurrences for elliptic hypergeometric integrals. Elliptic Integrable Systems. Rokko Lectures in Math. vol. 18 (2005), Kobe University 183-199
    • (2005) Rokko Lectures in Math. , vol.18 , pp. 183-199
    • Rains, E.M.1
  • 17
    • 33750631898 scopus 로고    scopus 로고
    • H. Rosengren, M. Schlosser, Elliptic determinant evaluations and the Macdonald identities for affine root systems, Compos. Math., in press
  • 18
    • 3543099119 scopus 로고
    • Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
    • Ruijsenaars S.N.M. Complete integrability of relativistic Calogero-Moser systems and elliptic function identities. Comm. Math. Phys. 110 (1987) 191-213
    • (1987) Comm. Math. Phys. , vol.110 , pp. 191-213
    • Ruijsenaars, S.N.M.1
  • 19
    • 84943473850 scopus 로고
    • Über die Darstellung der symmetrischen und der alternierenden Gruppe durch gebrochene lineare Substitutionen
    • Schur I. Über die Darstellung der symmetrischen und der alternierenden Gruppe durch gebrochene lineare Substitutionen. J. Reine Angew. Math. 139 (1911) 155-250
    • (1911) J. Reine Angew. Math. , vol.139 , pp. 155-250
    • Schur, I.1
  • 20
    • 0034348684 scopus 로고    scopus 로고
    • A proof of the Kac-Wakimoto affine denominator formula for the strange series
    • Zagier D. A proof of the Kac-Wakimoto affine denominator formula for the strange series. Math. Res. Lett. 7 (2000) 597-604
    • (2000) Math. Res. Lett. , vol.7 , pp. 597-604
    • Zagier, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.