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1: 34.10 Zeros
Such zeros are called trivial zeros. …
2: 25.10 Zeros
§25.10(i) Distribution
These are called the trivial zeros. Except for the trivial zeros, ζ ( s ) 0 for s 0 . …
3: 25.15 Dirichlet L -functions
Since L ( s , χ ) 0 if s > 1 , (25.15.5) shows that for a primitive character χ the only zeros of L ( s , χ ) for s < 0 (the so-called trivial zeros) are as follows: …
4: 18.33 Polynomials Orthogonal on the Unit Circle
Trivial
5: 24.16 Generalizations
Let χ 0 be the trivial character and χ 4 the unique (nontrivial) character with f = 4 ; that is, χ 4 ( 1 ) = 1 , χ 4 ( 3 ) = - 1 , χ 4 ( 2 ) = χ 4 ( 4 ) = 0 . …
6: Bibliography
  • T. M. Apostol (1985b) Note on the trivial zeros of Dirichlet L -functions. Proc. Amer. Math. Soc. 94 (1), pp. 29–30.
  • 7: 18.18 Sums