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Volumn 165, Issue 2, 2006, Pages 243-266

The f(q) mock theta function conjecture and partition ranks

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EID: 33745777166     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00222-005-0493-5     Document Type: Review
Times cited : (181)

References (27)
  • 2
    • 1642548355 scopus 로고
    • On the theorems of Watson and Dragonette for Ramanujan's mock theta functions
    • Andrews, G.E.: On the theorems of Watson and Dragonette for Ramanujan's mock theta functions. Am. J. Math. 88, 454-490 (1966)
    • (1966) Am. J. Math. , vol.88 , pp. 454-490
    • Andrews, G.E.1
  • 3
    • 0041031097 scopus 로고
    • Mock theta functions, Theta functions - Bowdoin 1987, part 2
    • (Brunswick, ME 1987) Providence, RI: Am. Math. Soc.
    • Andrews, G.E.: Mock theta functions, Theta functions - Bowdoin 1987, part 2 (Brunswick, ME 1987). Proc. Sympos. Pure Math. vol. 49, part 2, pp. 283-297. Providence, RI: Am. Math. Soc. 1989
    • (1989) Proc. Sympos. Pure Math. , vol.49 , Issue.2 PART , pp. 283-297
    • Andrews, G.E.1
  • 4
    • 1642500487 scopus 로고    scopus 로고
    • Partitions: At the interface of q-series and modular forms
    • Rankin Memorial Issues
    • Andrews, G.E.: Partitions: At the interface of q-series and modular forms. Rankin Memorial Issues, Ramanujan J. 7, 385-400 (2003)
    • (2003) Ramanujan J. , vol.7 , pp. 385-400
    • Andrews, G.E.1
  • 5
    • 16344365091 scopus 로고    scopus 로고
    • Partitions with short sequences and mock theta functions
    • Andrews, G.E.: Partitions with short sequences and mock theta functions. Proc. Natl. Acad. Sci. USA 102, 4666-4671 (2005)
    • (2005) Proc. Natl. Acad. Sci. USA , vol.102 , pp. 4666-4671
    • Andrews, G.E.1
  • 7
    • 0000594732 scopus 로고
    • Partitions and indefinite quadratic forms
    • Andrews, G.E., Dyson, F., Hickerson, D.: Partitions and indefinite quadratic forms. Invent. Math. 91, 391-407 (1988)
    • (1988) Invent. Math. , vol.91 , pp. 391-407
    • Andrews, G.E.1    Dyson, F.2    Hickerson, D.3
  • 10
    • 0141891762 scopus 로고    scopus 로고
    • Borcherds products on O(2,ℓ) and chern classes of heegner divisors
    • Berlin: Springer
    • Brainier, J.H.: Borcherds Products on O(2,ℓ) and Chern Classes of Heegner Divisors. Lect. Notes, vol. 1780. Berlin: Springer 2002
    • (2002) Lect. Notes , vol.1780
    • Brainier, J.H.1
  • 11
    • 7544227842 scopus 로고    scopus 로고
    • On two geometric theta lifts
    • Bruinier, J.H., Funke, J.: On two geometric theta lifts. Duke Math. J. 125, 45-90 (2004)
    • (2004) Duke Math. J. , vol.125 , pp. 45-90
    • Bruinier, J.H.1    Funke, J.2
  • 12
    • 0033472882 scopus 로고    scopus 로고
    • Tenth order mock theta functions in Ramanujan's lost notebook
    • Choi, Y.-S.: Tenth order mock theta functions in Ramanujan's lost notebook. Invent. Math. 136, 497-569 (1999)
    • (1999) Invent. Math. , vol.136 , pp. 497-569
    • Choi, Y.-S.1
  • 13
    • 0009877699 scopus 로고
    • Q-identities for Maass waveforms
    • Cohen, H.: q-identities for Maass waveforms. Invent. Math. 91, 409-422 (1988)
    • (1988) Invent. Math. , vol.91 , pp. 409-422
    • Cohen, H.1
  • 14
    • 33745792910 scopus 로고
    • Corrigendum to "q-identities for Maass waveforms"
    • Cohen, H.: Corrigendum to "q-identities for Maass waveforms". Invent. Math. 120, 579-580 (1995)
    • (1995) Invent. Math. , vol.120 , pp. 579-580
    • Cohen, H.1
  • 15
    • 0002930710 scopus 로고
    • Dimensions des espaces des formes modulaires
    • Springer
    • Cohen, H., Oesterlé, J.: Dimensions des espaces des formes modulaires. Lect. Notes, vol. 627, pp. 69-78. Springer 1977
    • (1977) Lect. Notes , vol.627 , pp. 69-78
    • Cohen, H.1    Oesterlé, J.2
  • 16
    • 84968484447 scopus 로고
    • Some asymptotic formulae for the mock theta series of Ramanujan
    • Dragonette, L.: Some asymptotic formulae for the mock theta series of Ramanujan. Trans. Am. Math. Soc. 72, 474-500 (1952)
    • (1952) Trans. Am. Math. Soc. , vol.72 , pp. 474-500
    • Dragonette, L.1
  • 17
    • 0001875065 scopus 로고
    • Some guesses in the theory of partitions
    • Dyson, F.: Some guesses in the theory of partitions. Eureka (Cambridge) 8, 10-15 (1944)
    • (1944) Eureka (Cambridge) , vol.8 , pp. 10-15
    • Dyson, F.1
  • 19
    • 0000950450 scopus 로고
    • On the seventh order mock theta functions
    • Hickerson, D.: On the seventh order mock theta functions. Invent. Math. 94, 661-677 (1988)
    • (1988) Invent. Math. , vol.94 , pp. 661-677
    • Hickerson, D.1
  • 20
    • 0039424978 scopus 로고
    • On the number of divisors of a quadratic polynomial
    • Hooley, C.: On the number of divisors of a quadratic polynomial. Acta Math. 110, 97-114 (1963)
    • (1963) Acta Math. , vol.110 , pp. 97-114
    • Hooley, C.1
  • 21
    • 27344441826 scopus 로고    scopus 로고
    • Partition congruences and the Andrews-Garvan-Dyson crank
    • Mahlburg, K.: Partition congruences and the Andrews-Garvan-Dyson crank. Proc. Natl. Acad. Sci. USA 102, 15373-15376 (2005)
    • (2005) Proc. Natl. Acad. Sci. USA , vol.102 , pp. 15373-15376
    • Mahlburg, K.1
  • 23
    • 33745780426 scopus 로고
    • The Lost Notebook and Other Unpublished Papers. New Delhi: Narosa
    • Ramanujan, S.: The Lost Notebook and Other Unpublished Papers. New Delhi: Narosa 1988
    • (1988)
    • Ramanujan, S.1
  • 24
    • 0001881731 scopus 로고
    • Modular forms of weight 1/2
    • Springer
    • Serre, J.-P., Stark, H.: Modular forms of weight 1/2. Lect. Notes, vol. 627, pp. 27-67. Springer 1977
    • (1977) Lect. Notes , vol.627 , pp. 27-67
    • Serre, J.-P.1    Stark, H.2
  • 25
    • 0000115411 scopus 로고
    • On modular forms of half integral weight
    • Shimura, G.: On modular forms of half integral weight. Ann. Math. 97, 440-481 (1973)
    • (1973) Ann. Math. , vol.97 , pp. 440-481
    • Shimura, G.1
  • 26
    • 0001952313 scopus 로고
    • The final problem: An account of the mock theta functions
    • Watson, G.N.: The final problem: An account of the mock theta functions. J. Lond. Math. Soc. 2, 55-80 (1936)
    • (1936) J. Lond. Math. Soc. , vol.2 , pp. 55-80
    • Watson, G.N.1
  • 27
    • 2142776307 scopus 로고    scopus 로고
    • Mock ν-functions and real analytic modular forms
    • q-Series with Applications to Combinatorics, Number Theory, and Physics, ed. by B.C. Berndt, K. Ono.
    • Zwegers, S.P.: Mock ν-functions and real analytic modular forms. q-Series with Applications to Combinatorics, Number Theory, and Physics, ed. by B.C. Berndt, K. Ono. Contemp. Math. 291, 269-277 (2001)
    • (2001) Contemp. Math. , vol.291 , pp. 269-277
    • Zwegers, S.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.