Zeros of quadratic zeta-functions on the critical line

A. Sankaranarayanan

Acta Arithmetica (1995)

  • Volume: 69, Issue: 1, page 21-38
  • ISSN: 0065-1036

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A. Sankaranarayanan. "Zeros of quadratic zeta-functions on the critical line." Acta Arithmetica 69.1 (1995): 21-38. <http://eudml.org/doc/206670>.

@article{A1995,
author = {A. Sankaranarayanan},
journal = {Acta Arithmetica},
keywords = {gaps; zeta-function; ideal class; imaginary quadratic field; Epstein zeta-function; binary quadratic form; critical line; zeros},
language = {eng},
number = {1},
pages = {21-38},
title = {Zeros of quadratic zeta-functions on the critical line},
url = {http://eudml.org/doc/206670},
volume = {69},
year = {1995},
}

TY - JOUR
AU - A. Sankaranarayanan
TI - Zeros of quadratic zeta-functions on the critical line
JO - Acta Arithmetica
PY - 1995
VL - 69
IS - 1
SP - 21
EP - 38
LA - eng
KW - gaps; zeta-function; ideal class; imaginary quadratic field; Epstein zeta-function; binary quadratic form; critical line; zeros
UR - http://eudml.org/doc/206670
ER -

References

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  1. [1] R. Balasubramanian, An improvement of a theorem of Titchmarsh on the mean square of |ζ(1/2 +it)|, Proc. London Math. Soc. (3) 36 (1978), 540-576. Zbl0375.10025
  2. [2] R. Balasubramanian and K. Ramachandra, Proof of some conjectures on the mean-value of Titchmarsh series. I, Hardy-Ramanujan J. 13 (1990), 1-20. Zbl0733.11027
  3. [3] B. C. Berndt, The number of zeros of the Dedekind zeta-function on the critical line, J. Number Theory 3 (1971), 1-6. Zbl0208.31102
  4. [4] K. Chandrasekharan and R. Narasimhan, Zeta-functions of ideal classes in quadratic fields and their zeros on the critical line, Comment. Math. Helv. 43 (1968), 18-30. Zbl0157.09302
  5. [5] E. Hecke, Über Dirichlet-Reihen mit Funktionalgleichung und ihre Nullstellen auf der Mittelgeraden, München Akad. Sitzungsber. II, 8 (1937), 73-95. Zbl0018.21002
  6. [6] E. Hecke, Über die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung, Math. Ann. 112 (1936), 664-699. Zbl0014.01601
  7. [7] E. Landau, Vorlesungen über Zahlentheorie, VII. Teil, Kap. 7, Chelsea, 1947. 
  8. [8] H. S. A. Potter, Approximate equations for the Epstein zeta-function, Proc. London Math. Soc. (2) 36 (1934), 501-515. Zbl0008.30001
  9. [9] H. S. A. Potter and E. C. Titchmarsh, The zeros of Epstein's zeta-functions, Proc. London Math. Soc. 39 (1935), 372-384. Zbl0011.39101
  10. [10] K. Ramachandra, Progress towards a conjecture on the mean-value of Titchmarsh series, in: Recent Progress in Analytic Number Theory, H. Halberstam and C. Hooley (eds.), Vol. 1, Academic Press, 1981, 303-318. 
  11. [11] H. M. Stark, L-functions and character sums for quadratic forms (I), Acta Arith. 14 (1968), 35-50. Zbl0198.37801
  12. [12] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, 2nd ed., revised by D. R. Heath-Brown, Oxford Sci. Publ., Clarendon Press, Oxford, 1986. Zbl0601.10026

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