On the values of the Epstein zeta function
1973 ◽
Vol 14
(1)
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pp. 1-12
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Keyword(s):
Let ζ(s) = σn-s(Res >1) denote the Riemann zeta function; then, as is well known,, whereBmdenotes themth Bernoulli number, In this paper we investigate the possibility of similar evaluations of the Epstein zeta function ζq(s) at the rational integerss = k> 2. Letbe a positive definite quadratic form andwhere the summation is over all pairs of integers except (0, 0). In attempting to evaluate ζq(k) we are guided by Kronecker's first limit formula [11]where γ is Euler's constant,is the Dedekind eta-function, and τ is the complex number in the upper half plane, ℋ, associated with Q by the formulaOn the basis of (1.3) we would expect a formula involving functions of τ. This formula is stated in Theorem 1, (2.13).
1964 ◽
Vol 6
(4)
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pp. 198-201
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1959 ◽
Vol 4
(2)
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pp. 73-80
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1988 ◽
Vol 30
(1)
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pp. 75-85
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1964 ◽
Vol 60
(4)
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pp. 855-875
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Keyword(s):
1932 ◽
Vol 28
(3)
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pp. 273-274
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Keyword(s):
1935 ◽
Vol 54
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pp. 12-16
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2013 ◽
Vol 97
(540)
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pp. 455-460
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1959 ◽
Vol 1
(1)
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pp. 47-63
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Keyword(s):
1967 ◽
Vol 15
(4)
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pp. 309-313
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1978 ◽
Vol 21
(1)
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pp. 25-32
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Keyword(s):