Geodesic
Around the Davenport–Heilbronn function
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 66 (2011) no. 2, pp. 221-270 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper deals with analytic properties of certain Dirichlet series considered by Davenport and Heilbronn and by Titchmarsh. Bibliography: 28 titles.
Keywords: zeros of Dirichlet series, reciprocals of Dirichlet series, estimates of coefficients. 
@article{RM_2011_66_2_a1,
     author = {E. Bombieri and A. Ghosh},
     title = {Around the {Davenport{\textendash}Heilbronn} function},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {221--270},
     year = {2011},
     volume = {66},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2011_66_2_a1/}
}
TY  - JOUR
AU  - E. Bombieri
AU  - A. Ghosh
TI  - Around the Davenport–Heilbronn function
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2011
SP  - 221
EP  - 270
VL  - 66
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/RM_2011_66_2_a1/
LA  - en
ID  - RM_2011_66_2_a1
ER  - 
%0 Journal Article
%A E. Bombieri
%A A. Ghosh
%T Around the Davenport–Heilbronn function
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2011
%P 221-270
%V 66
%N 2
%U http://geodesic.mathdoc.fr/item/RM_2011_66_2_a1/
%G en
%F RM_2011_66_2_a1
E. Bombieri; A. Ghosh. Around the Davenport–Heilbronn function. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 66 (2011) no. 2, pp. 221-270. http://geodesic.mathdoc.fr/item/RM_2011_66_2_a1/

[1] H. Hamburger, “Über die Riemannsche Funktionalgleichung der $\zeta$-Funktion. I”, Math. Z., 10 (1921), 240–254 | DOI | MR | Zbl

[2] H. S. A. Potter, E. C. Titchmarsh, “The zeros of Epstein's zeta functions”, Proc. London Math. Soc. (2), 39 (1935), 372–384 | DOI | Zbl

[3] H. Davenport, H. Heilbronn, “On the zeros of certain Dirichlet series”, J. London Math. Soc., 11 (1936), 181–185 | DOI | Zbl

[4] H. Davenport, H. Heilbronn, “On the zeros of certain Dirichlet series. II”, J. London Math. Soc., 11 (1936), 307–312 | DOI | Zbl

[5] J. W. S. Cassels, “Footnote to a note of Davenport and Heilbronn”, J. London Math. Soc., 36 (1961), 177–184 | DOI | MR | Zbl

[6] H. M. Stark, “The Gauss class-number problems”, Analytic number theory, Clay Math. Proc., 7, Amer. Math. Soc., Providence, RI, 2007, 247–256 | MR | Zbl

[7] E. Bombieri, “The classical theory of zeta and $L$-functions”, Milan J. Math., 78:1 (2010), 11–59 | DOI | MR | Zbl

[8] A. Selberg, “On the zeros of Riemann's zeta-function”, Skr. Norske Vid. Akad. Oslo I, 1942:10 (1942), 59 pp. ; Collected papers, v. I, Springer-Verlag, Berlin, 1989, 85–141 | MR | Zbl | MR | Zbl

[9] S. M. Voronin, “On the zeros of some Dirichlet series lying on the critical line”, Math. USSR-Izv., 16:1 (1981), 55–82 | DOI | MR | Zbl

[10] E. C. Titchmarsh, The theory of the Riemann zeta-function, 2nd edition, The Clarendon Press, Oxford Univ. Press, New York, 1986, 412 pp. | MR | Zbl

[11] A. A. Karatsuba, “On zeros of the Davenport–Heilbronn function”, Proceedings of the Amalfi Conference on Analytic Number Theory (Maiori, 1989), Univ. Salerno, Salerno, 1992, 271–293 | MR | Zbl

[12] E. Bombieri, D. A. Hejhal, “On the distribution of zeros of linear combination of Euler products”, Duke Math. J., 80:3 (1995), 821–862 | DOI | MR | Zbl

[13] H. Bohr, “Über das Verhalten von $\zeta(s)$ in der Halbebene $\sigma>1$”, Gött. Nachr., 1911, 409–428 | Zbl

[14] H. Davenport, The collected works of Harold Davenport, v. I–IV, eds. B. J. Birch, H. Halberstam, C. A. Rogers, Academic Press, London–New York–San Francisco, 1977, 1910 pp. | MR | Zbl

[15] B. Jessen, H. Tornehave, “Mean motions and zeros of almost periodic functions”, Acta Math., 77:1 (1945), 137–279 | DOI | MR | Zbl

[16] V. Borchsenius, B. Jessen, “Mean motions and values of the Riemann zeta function”, Acta Math., 80:1 (1948), 97–166 | DOI | MR | Zbl

[17] S. M. Gonek, “The zeros of Hurwitz's zeta function on $\sigma=\frac{1}{2}$”, Analytic number theory (Philadelphia, PA, 1980), Lecture Notes in Math., 899, Springer, Berlin–New York, 1981, 129–140 | DOI | MR | Zbl

[18] E. Bombieri, J. Mueller, “On the zeros of certain Epstein zeta functions”, Forum Math., 20:2 (2008), 359–385 | DOI | MR | Zbl

[19] Yoonbok Lee, On the zeros of Epstein zeta functions, Preprint, 2010

[20] S. M. Voronin, “The zeros of zeta-functions of quadratic forms”, Proc. Steklov Inst. Math., 142 (1979), 143–155 | MR | Zbl

[21] A. A. Karatsuba, S. M. Voronin, The Riemann zeta-function, de Gruyter Exp. Math., 5, de Gruyter, Berlin, 1992, 396 pp. | MR | MR | Zbl | Zbl

[22] S. M. Voronin, “Theorem on the ‘universality’ of the Riemann zeta-function”, Math. USSR-Izv., 9:3 (1975), 443–453 | DOI | MR | Zbl | Zbl

[23] A. Laurinčikas, Limit theorems for the Riemann zeta-function, Math. Appl., 352, Kluwer, Dordrecht, 1996, xiii+297 pp. | MR | Zbl

[24] E. Landau, “Über den Wertevorrat von $\zeta(s)$ in der Halbebene $\sigma > 1$”, Nachr. Ges. Wiss. Göttingen, 1933, no. 36, 81–91 ; Edmund Landau collected works, 9, Thales Verlag, Essen, 1987, 243–255 | Zbl

[25] E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Chelsea Publishing Co., New York, 1953, xviii + pp. 1–564; ix + pp. 565–1001 | MR | Zbl

[26] E. Hille, “The inversion problem of Möbius”, Duke Math. J., 3:4 (1937), 549–568 | DOI | MR | Zbl

[27] E. Hille, “A problem in ‘factorisatio numerorum’ ”, Acta Arith., 2 (1936), 134–144 | Zbl

[28] F. Carlson, “Über die Nullstellen der Dirichletschen Reihen und der Riemannschen $\zeta$-Funktion”, Arkiv för Mat. Astr. och Fysik, 15:20 (1921), 28 pp. | Zbl