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- W2074583470 abstract "Let L k ( S ) be the product of the ϕ( k ) Dirichlet L -functions formed with characters modulo k . We prove the existence of explicit numerical zero-free regions for L k ( S ). The first result is that L k ( S ) has at most a single zero in the region { s: σ > 1 − 1 (R log M) } , where R = 9.645908801 and M = max { k , k | t |, 10}. The only possible zero in this region is a simple real zero arising from an L -function formed with a real non-principal character. The second result is that if χ 1 and χ 2 are distinct real primitive characters modulo k 1 and k 2 , respectively, and if β 1 is a zero of L ( s , χ i ), i = 1, 2, then min {β 1 , β 2 } < 1 − 1 (R 1 log M 1 ) , where R 1 = (5 − √5) (15 − 10√2) , and M 1 = max { k 1 k 2 17 , 13} ." @default.
- W2074583470 created "2016-06-24" @default.
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- W2074583470 date "1984-08-01" @default.
- W2074583470 modified "2023-09-30" @default.
- W2074583470 title "Explicit zero-free regions for Dirichlet L-functions" @default.
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- W2074583470 doi "https://doi.org/10.1016/0022-314x(84)90089-1" @default.
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