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Volumn 97, Issue 2, 2001, Pages 157-172

On an asymptotic formula of Ramanujan for a certain theta-type series

Author keywords

Asymptotic expansion; Hurwitz zeta function; Lerch zeta function; Mellin transform; Multiple zeta function; Riemann zeta function; Theta series

Indexed keywords


EID: 0035649442     PISSN: 00651036     EISSN: None     Source Type: Journal    
DOI: 10.4064/aa97-2-4     Document Type: Article
Times cited : (22)

References (21)
  • 1
    • 84972529289 scopus 로고
    • On the Lerch zeta function
    • T. M. Apostol, On the Lerch zeta function, Pacific J. Math. 1 (1951), 161-167.
    • (1951) Pacific J. Math. , vol.1 , pp. 161-167
    • Apostol, T.M.1
  • 3
    • 0000457764 scopus 로고
    • The theory of the multiple gamma function
    • E. W. Barnes, The theory of the multiple gamma function, Trans. Cambridge Philos. Soc. 19 (1904), 265-387.
    • (1904) Trans. Cambridge Philos. Soc. , vol.19 , pp. 265-387
    • Barnes, E.W.1
  • 5
    • 0007263127 scopus 로고
    • Chapter 15 of Ramanujan's second notebook: Part II, modular forms
    • B. C. Berndt and R. J. Evans, Chapter 15 of Ramanujan's Second Notebook: Part II, Modular forms, Acta Arith. 47 (1986), 123-142.
    • (1986) Acta Arith. , vol.47 , pp. 123-142
    • Berndt, B.C.1    Evans, R.J.2
  • 6
    • 0007275758 scopus 로고
    • χ-analogue of a formula of Ramanujan for ζ(1/2)
    • χ-analogue of a formula of Ramanujan for ζ(1/2), ibid. 69 (1995), 189-191.
    • (1995) Acta Arith. , vol.69 , pp. 189-191
    • Egami, S.1
  • 9
    • 21344452031 scopus 로고    scopus 로고
    • Power series with the Riemann zeta-function in the coefficients
    • M. Katsurada, Power series with the Riemann zeta-function in the coefficients, Proc. Japan Acad. Ser. A 72 (1996), 61-63.
    • (1996) Proc. Japan Acad. Ser. A , vol.72 , pp. 61-63
    • Katsurada, M.1
  • 10
    • 0007191331 scopus 로고    scopus 로고
    • On Mellin-Barnes type of integrals and sums associated with the Riemann zeta-function
    • N.S.
    • _, On Mellin-Barnes type of integrals and sums associated with the Riemann zeta-function, Publ. Inst. Math. (Beograd) (N.S.) 62(76) (1997), 13-25.
    • (1997) Publ. Inst. Math. (Beograd) , vol.62 , Issue.76 , pp. 13-25
  • 11
    • 0000905880 scopus 로고    scopus 로고
    • An application of Mellin-Barnes' type integrals to the mean square of Lerch zeta-functions
    • _, An application of Mellin-Barnes' type integrals to the mean square of Lerch zeta-functions, Collect. Math. 48 (1997), 137-153.
    • (1997) Collect. Math. , vol.48 , pp. 137-153
  • 12
    • 0007275759 scopus 로고    scopus 로고
    • An application of Mellin-Barnes type of integrals to the mean square of L-functions
    • _, An application of Mellin-Barnes type of integrals to the mean square of L-functions, Liet. Mat. Rink. 38 (1998), 98-112.
    • (1998) Liet. Mat. Rink. , vol.38 , pp. 98-112
  • 13
    • 22444452123 scopus 로고    scopus 로고
    • Power series and asymptotic series associated with the Lerch zeta-function
    • _, Power series and asymptotic series associated with the Lerch zeta-function, Proc. Japan Acad. Ser. A 74 (1998), 167-170.
    • (1998) Proc. Japan Acad. Ser. A , vol.74 , pp. 167-170
  • 14
    • 0001799697 scopus 로고    scopus 로고
    • χ-analogue
    • χ-analogue, Acta Arith. 90 (1999), 79-89.
    • (1999) Acta Arith. , vol.90 , pp. 79-89
  • 15
    • 0007259233 scopus 로고
    • On entry 8 of chapter 15 of Ramanujan's notebook II
    • D. Klusch, On Entry 8 of Chapter 15 of Ramanujan's Notebook II, ibid. 58 (1991), 59-64.
    • (1991) Acta Arith. , vol.58 , pp. 59-64
    • Klusch, D.1
  • 18
    • 0004220292 scopus 로고
    • 2 volumes, Tata Institute of Fundamental Research, Bombay
    • S. Ramanujan, Notebooks, 2 volumes, Tata Institute of Fundamental Research, Bombay, 1957.
    • (1957) Notebooks
    • Ramanujan, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.