On small zeros of Dirichlet functions
Author:
Peter J. Weinberger
Journal:
Math. Comp. 29 (1975), 319328
MSC:
Primary 10H10; Secondary 1004
MathSciNet review:
0376564
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Abstract: A method is given for calculating the value of Dirichlet Lfunctions near the real axis in the critical strip. As an application, some zeros for zeta functions of complex quadratic fields are calculated.
 [1]
J.
Barkley Rosser, J.
M. Yohe, and Lowell
Schoenfeld, Rigorous computation and the zeros of the Riemann
zetafunction. (With discussion), Information Processing 68 (Proc.
IFIP Congress, Edinburgh, 1968) NorthHolland, Amsterdam, 1969,
pp. 70–76. MR 0258245
(41 #2892)
 [2]
H.
L. Montgomery and P.
J. Weinberger, Notes on small class numbers, Acta Arith.
24 (1973/74), 529–542. Collection of articles
dedicated to Carl Ludwig Siegel on the occasion of his seventyfifth
birthday, V. MR
0357373 (50 #9841)
 [3]
D.
Davies and C.
B. Haselgrove, The evaluation of Dirichlet
𝐿functions, Proc. Roy. Soc. Ser. A 264
(1961), 122–132. MR 0136052
(24 #B2091)
 [4]
D.
Davies, An approximate functional equation for Dirichlet
𝐿functions, Proc. Roy. Soc. Ser. A 284
(1965), 224–236. MR 0173352
(30 #3565)
 [5]
D.
H. Lehmer, Extended computation of the Riemann zetafunction,
Mathematika 3 (1956), 102–108. MR 0086083
(19,121b)
 [6]
Milton
Abramowitz and Irene
A. Stegun, Handbook of mathematical functions with formulas,
graphs, and mathematical tables, National Bureau of Standards Applied
Mathematics Series, vol. 55, For sale by the Superintendent of
Documents, U.S. Government Printing Office, Washington, D.C., 1964. MR 0167642
(29 #4914)
 [7]
A.
H. Stroud and Don
Secrest, Gaussian quadrature formulas, PrenticeHall, Inc.,
Englewood Cliffs, N.J., 1966. MR 0202312
(34 #2185)
 [8]
Harold
Davenport, Multiplicative number theory, Lectures given at the
University of Michigan, Winter Term, vol. 1966, Markham Publishing
Co., Chicago, Ill., 1967. MR 0217022
(36 #117)
 [9]
M.
E. Low, Real zeros of the Dedekind zeta function of an imaginary
quadratic field, Acta Arith 14 (1967/1968),
117–140. MR 0236127
(38 #4425)
 [10]
G. PURDY, "The real zeros of the Epstein zeta function." (To appear).
 [1]
 J. B. ROSSER, J. M. YOHE & L. SCHOENFELD, "Rigorous computation and the zeros of the Riemann zetafunction," Proc. IFIP Congress (Edinburgh, 1968), vol. 1: Mathematics, Software, NorthHolland, Amsterdam, 1969, pp. 7076. MR 41 #2892. MR 0258245 (41:2892)
 [2]
 H. L. MONTGOMERY & P. J. WEINBERGER, "Notes on small class numbers," Acta Arith., v. 24, 1974, pp. 529542. MR 0357373 (50:9841)
 [3]
 D. DAVIES & C. B. HASELGROVE, "The evaluation of Dirichlet Lfunctions," Proc. Roy. Soc. Ser. A, v. 264, 1961, pp. 122132. MR 24 #B2091. MR 0136052 (24:B2091)
 [4]
 D. DAVIES, "An approximate functional equation for Dirichlet Lfunctions," Proc. Roy. Soc. Ser. A, v. 284, 1965, pp. 224236. MR 30 #3565. MR 0173352 (30:3565)
 [5]
 D. H. LEHMER, "Extended computation of the Riemann zetafunction," Mathematika, v. 3, 1956, pp. 102108. MR 19, 121; 1431. MR 0086083 (19:121b)
 [6]
 M. ABRAMOWITZ & I. A. STEGUN (Editors), Handbook of Mathematical Functions, With Formulas, Graphs and Mathematical Tables, 3rd printing with corrections, Nat. Bur. Standards Appl. Math. Series, 55, Superintendent of Documents, U. S. Government Printing Office, Washington, D. C., 1965. MR 31 #1400. MR 0167642 (29:4914)
 [7]
 A. H. STROUD & D. SECREST, Gaussian Quadrature Formulas, PrenticeHall, Englewood Cliffs, N. J., 1966. MR 34 #2185. MR 0202312 (34:2185)
 [8]
 H. DAVENPORT, Multiplicative Number Theory, Lectures in Advanced Math., no. 1, Markham, Chicago, Ill., 1967. MR 36 #117. MR 0217022 (36:117)
 [9]
 M. E. LOW, "Real zeros of the Dedekind zeta function of an imaginary quadratic field," Acta. Arith., v. 14, 1967/68, pp. 117140. MR 38 #4425. MR 0236127 (38:4425)
 [10]
 G. PURDY, "The real zeros of the Epstein zeta function." (To appear).
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197503765647
PII:
S 00255718(1975)03765647
Article copyright:
© Copyright 1975
American Mathematical Society
