Skip to main content
SpringerLink
Log in

On the frequency of Titchmarsh’s phenomenon for ζ(s)-VIII

  • Published:
Proceedings of the Indian Academy of Sciences - Mathematical Sciences Aims and scope Submit manuscript

Abstract

For suitable functionsH = H(T) the maximum of¦(ζ(σ + it)) z ¦ taken overT≤t≤T + H is studied. For fixed σ(1/2≤σ≤l) and fixed complex constantsz “expected lower bounds” for the maximum are established.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Balasubramanian R, An improvement on a theorem of Titchmarsh on the mean-square of ¦ζ(1/2 +it)¦, Proc. London Math. Soc. 36 (1978) 540–576

    Article  MATH  MathSciNet  Google Scholar 

  2. Balasubramanian R and Ramachandra K, Progress towards a conjecture on the mean-value of Titchmarsh series-III,Acta Arith., XLV (1986) 309–318

    MathSciNet  Google Scholar 

  3. Levinson N, Ω-theorems for the Riemann zeta-function,Acta Arith. XX (1972) 319–332

    MathSciNet  Google Scholar 

  4. Montgomery H L, Extreme values of the Reimann zeta-function,Comm. Math. Helv. 52 (1977) 511–518

    Article  MATH  Google Scholar 

  5. Ramachandra K, Progress towards a conjecture on the mean-value of Titchmarsh series-I, in: Recent progress in analytic number theory (eds) H Halberstam and C Hooley (1981) Vol. I, (London: Academic Press), 303–318

    Google Scholar 

  6. Ramachandra K, On the frequency of Titchmarsh’s phenomenon for ζ(s)-I,J-London Math, Soc. 8 (1974) 683–690

    Article  MATH  MathSciNet  Google Scholar 

  7. Ramachandra K, On the frequency of Titchmarsh’s phenomenon for ζ(s)-VII,Ann. Acad. Sci. Fenn. Ser. A1. Mathematica 14 (1989) 27–40

    MathSciNet  Google Scholar 

  8. Ramachandra K and Sankaranarayanan A,Note on a paper by H L MontgomeryPubl. L’Inst. Math. (Beograd) 50 (64) (1991) 51–59

    MathSciNet  Google Scholar 

  9. Titchmarsh E C, The theory of the Riemann zeta-function, (Oxford: Clarendon Press) (1951)

    MATH  Google Scholar 

References added in proof

  1. R Balasubramanian,On the frequency of Titchmarsh’s phenomenon for ζ (s) -IV,Hardy-Ramanujan J,9 (1986), 1–10

    MATH  MathSciNet  Google Scholar 

  2. K Ramachandra,On the frequency of Titchmarsh’s phenomenon for ζ(s)-IX,Hardy-Ramanujan J,13 (1990), 28–33

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Institute of Mathematical Sciences, 600113, Madras, India

    R. Balasubramanian, K. Ramachandra & A. Sankaranarayanan

  2. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, 400005, Bombay, India

    K. Ramachandra & A. Sankaranarayanan

Authors
  1. R. Balasubramanian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Ramachandra
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Sankaranarayanan
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Balasubramanian, R., Ramachandra, K. & Sankaranarayanan, A. On the frequency of Titchmarsh’s phenomenon for ζ(s)-VIII. Proc. Indian Acad. Sci. (Math. Sci.) 102, 1–12 (1992). https://doi.org/10.1007/BF02837174

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02837174

Keywords

Search

Navigation