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Volumn 77, Issue 263, 2008, Pages 1681-1694

Sign changes in sums of the Liouville function

Author keywords

Liouville function; Polya's sum; Riemann hypothesis; Turan's sum

Indexed keywords


EID: 47249097549     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-08-02036-X     Document Type: Article
Times cited : (31)

References (20)
  • 1
    • 0042188486 scopus 로고
    • Oscillation theorems, Analytic Number Theory
    • Philadelphia, Springer, Berlin, MR654520 83h:10082
    • R. J. Anderson and H. M. Stark, Oscillation theorems, Analytic Number Theory (Philadelphia, 1980), Lecture Notes in Math., vol. 899, Springer, Berlin, 1981, pp. 79-106. MR654520 (83h:10082)
    • (1980) Lecture Notes in Math , vol.899 , pp. 79-106
    • Anderson, R.J.1    Stark, H.M.2
  • 2
    • 47249142992 scopus 로고    scopus 로고
    • P. T. Bateman and S. Chowla, The equivalence of two conjectures in the theory of numbers, J. Indian Math. Soc. (N.S.) 17 (1953), 177-181 (1954). MR0062176 (15:939c)
    • P. T. Bateman and S. Chowla, The equivalence of two conjectures in the theory of numbers, J. Indian Math. Soc. (N.S.) 17 (1953), 177-181 (1954). MR0062176 (15:939c)
  • 3
    • 0039648567 scopus 로고    scopus 로고
    • Computing the summation of the Möbius function
    • MR1437219 98f:11135
    • M. Deléglise and J. Rivat, Computing the summation of the Möbius function, Experiment. Math. 5 (1996), no. 4, 291-295. MR1437219 (98f:11135)
    • (1996) Experiment. Math , vol.5 , Issue.4 , pp. 291-295
    • Deléglise, M.1    Rivat, J.2
  • 5
    • 47249125460 scopus 로고    scopus 로고
    • A. Granville and K. Soundararajan, Negative values of truncations to L(1, χ), Proceedings of the Gauss-Dirichlet Conference (Göttingen, 2005), Clay Math. Proceedings, 7, Amer. Math. Soc., Providence, 2007.
    • A. Granville and K. Soundararajan, Negative values of truncations to L(1, χ), Proceedings of the Gauss-Dirichlet Conference (Göttingen, 2005), Clay Math. Proceedings, vol. 7, Amer. Math. Soc., Providence, 2007.
  • 6
    • 47249131343 scopus 로고
    • On a table of values of L(n)
    • MR0003644 2:248i
    • H. Gupta, On a table of values of L(n), Proc. Indian Acad. Sci., Sect. A. 12 (1940), 407-409. MR0003644 (2:248i)
    • (1940) Proc. Indian Acad. Sci., Sect. A , vol.12 , pp. 407-409
    • Gupta, H.1
  • 8
    • 84971177626 scopus 로고
    • A disproof of a conjecture of Pólya
    • MR0104638 21:3391
    • _, A disproof of a conjecture of Pólya, Mathematika 5 (1958), 141-145. MR0104638 (21:3391)
    • (1958) Mathematika , vol.5 , pp. 141-145
    • Haselgrove, C.B.1
  • 10
    • 4644310093 scopus 로고
    • On two conjectures in the theory of numbers
    • MR0006202 3:271c
    • A. E. Ingham, On two conjectures in the theory of numbers, Amer. J. Math. 64 (1942), 313-319. MR0006202 (3:271c)
    • (1942) Amer. J. Math , vol.64 , pp. 313-319
    • Ingham, A.E.1
  • 11
    • 47249123815 scopus 로고    scopus 로고
    • O. Larsen, Epreuve numérique d'une supposition de P. Turán, Mat. Tidsskr. B. 1952 (1952), 28. MR0053962 (14:847c)
    • O. Larsen, Epreuve numérique d'une supposition de P. Turán, Mat. Tidsskr. B. 1952 (1952), 28. MR0053962 (14:847c)
  • 12
    • 84968503862 scopus 로고
    • On Liouville's function
    • MR0120198 22:10955
    • R. S. Lehman, On Liouville's function, Math. Comp. 14 (1960), 311-320. MR0120198 (22:10955)
    • (1960) Math. Comp , vol.14 , pp. 311-320
    • Lehman, R.S.1
  • 14
    • 0042671400 scopus 로고    scopus 로고
    • M. R. Murty and A. Sankaranarayanan, Averages of exponential twists of the Liouville function, Forum Math. 14 (2002), no. 2, 273-291. MR1880914 (2002m:11078)
    • M. R. Murty and A. Sankaranarayanan, Averages of exponential twists of the Liouville function, Forum Math. 14 (2002), no. 2, 273-291. MR1880914 (2002m:11078)
  • 15
    • 4243415234 scopus 로고
    • Verschiedene Bemerkungen zur Zahlentheorie
    • G. Pólya, Verschiedene Bemerkungen zur Zahlentheorie, Jahresber. Deutsch. Math.-Verein. 28 (1919), 31-40.
    • (1919) Jahresber. Deutsch. Math.-Verein , vol.28 , pp. 31-40
    • Pólya, G.1
  • 16
    • 0040553580 scopus 로고
    • Mersenne and Fermat numbers
    • MR0064787 16:335d
    • R. M. Robinson, Mersenne and Fermat numbers, Proc. Amer. Math. Soc. 5 (1954), 842-846. MR0064787 (16:335d)
    • (1954) Proc. Amer. Math. Soc , vol.5 , pp. 842-846
    • Robinson, R.M.1
  • 17
    • 84972492863 scopus 로고
    • A numerical investigation on cumulative sum of the Liouville function
    • MR584557 83h:10010
    • M. Tanaka, A numerical investigation on cumulative sum of the Liouville function, Tokyo J. Math. 3 (1980), no. 1, 187-189. MR584557 (83h:10010)
    • (1980) Tokyo J. Math , vol.3 , Issue.1 , pp. 187-189
    • Tanaka, M.1
  • 18
    • 47249107013 scopus 로고
    • On some approximative Dirichlet-polynomials in the theory of the zeta-function of Riemann
    • MR0027305 10:286a
    • P. Turán, On some approximative Dirichlet-polynomials in the theory of the zeta-function of Riemann, Danske Vid. Selsk. Mat.-Fys. Medd. 24 (1948), no. 17, 1-36. MR0027305 (10:286a)
    • (1948) Danske Vid. Selsk. Mat.-Fys. Medd , vol.24 , Issue.17 , pp. 1-36
    • Turán, P.1
  • 19
    • 34250594125 scopus 로고
    • Nachtrag zu meiner Abhandlung "On some approximative Dirichlet polynomials in the theory of zeta-function of Riemann
    • MR0115977 22:6774
    • _, Nachtrag zu meiner Abhandlung "On some approximative Dirichlet polynomials in the theory of zeta-function of Riemann", Acta Math. Acad. Sci. Hungar. 10 (1959), 277-298. MR0115977 (22:6774)
    • (1959) Acta Math. Acad. Sci. Hungar , vol.10 , pp. 277-298
    • Turán, P.1
  • 20
    • 51249193361 scopus 로고
    • Notes on Pólya's and Turán's hypotheses concerning Liouville's factor
    • MR0099319 20:5759
    • N. Wiener and A. Wintner, Notes on Pólya's and Turán's hypotheses concerning Liouville's factor, Rend. Circ. Mat. Palermo (2) 6 (1957), 240-248. MR0099319 (20:5759)
    • (1957) Rend. Circ. Mat. Palermo (2) , vol.6 , pp. 240-248
    • Wiener, N.1    Wintner, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.