|
On small zeros of Dirichlet -functions
Author:
Peter J. Weinberger
Journal:
Math. Comp. 29 (1975), 319-328
MSC:
Primary 10H10; Secondary 10-04
MathSciNet review:
0376564
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: A method is given for calculating the value of Dirichlet L-functions 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
zeta-function. (With discussion), Information Processing 68 (Proc.
IFIP Congress, Edinburgh, 1968) North-Holland, 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 seventy-fifth
birthday, V. MR
0357373 (50 #9841)
- [3]
D.
Davies and C.
B. Haselgrove, The evaluation of Dirichlet
𝐿-functions, Proc. Roy. Soc. Ser. A 264
(1961), 122–132. MR 0136052
(24 #B2091)
- [4]
D.
Davies, An approximate functional equation for Dirichlet
𝐿-functions, Proc. Roy. Soc. Ser. A 284
(1965), 224–236. MR 0173352
(30 #3565)
- [5]
D.
H. Lehmer, Extended computation of the Riemann zeta-function,
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, Prentice-Hall 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 zeta-function," Proc. IFIP Congress (Edinburgh, 1968), vol. 1: Mathematics, Software, North-Holland, Amsterdam, 1969, pp. 70-76. 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. 529-542. MR 0357373 (50:9841)
- [3]
- D. DAVIES & C. B. HASELGROVE, "The evaluation of Dirichlet L-functions," Proc. Roy. Soc. Ser. A, v. 264, 1961, pp. 122-132. MR 24 #B2091. MR 0136052 (24:B2091)
- [4]
- D. DAVIES, "An approximate functional equation for Dirichlet L-functions," Proc. Roy. Soc. Ser. A, v. 284, 1965, pp. 224-236. MR 30 #3565. MR 0173352 (30:3565)
- [5]
- D. H. LEHMER, "Extended computation of the Riemann zeta-function," Mathematika, v. 3, 1956, pp. 102-108. 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, Prentice-Hall, 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. 117-140. MR 38 #4425. MR 0236127 (38:4425)
- [10]
- G. PURDY, "The real zeros of the Epstein zeta function." (To appear).
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
10H10,
10-04
Retrieve articles in all journals
with MSC:
10H10,
10-04
Additional Information
DOI:
http://dx.doi.org/10.1090/S0025-5718-1975-0376564-7
PII:
S 0025-5718(1975)0376564-7
Article copyright:
© Copyright 1975 American Mathematical Society
|