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- Cho, Peter J.
- Lab for L-functions and arithmetic
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The smallest prime in a conjugacy class and the first sign change for automorphic L-functions
- Author(s)
- Cho, Peter J., Kim, Henry H.
- Issued Date
- 2021-03
- Citation
- PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, v.149, no.3, pp.923 - 933
- Abstract
- Let K be an S-n-field. For a nonidentity conjugacy class C, define N-K,N-C to be the smallest prime p such that Frob(p) is an element of C. By using the observation that N-K,N-C is interpreted as the first prime sign change of the Dirichlet coefficients of automorphic L-functions, we improve the known bound on N-K,N-C for n = 3, 4, 5. (For n = 5, we need to assume the strong Artin conjecture.)
- Publisher
- AMER MATHEMATICAL SOC
- ISSN
- 0002-9939
- Keyword (Author)
- Linnik problems, smallest prime in a conjugacy class, Artin L-function
- Keyword
- LEAST PRIME
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