Journal of the Ramanujan Mathematical Society

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A Variation on the Solvable Case of the Dedekind Conjecture


Affiliations
1 American University, Washington, DC 20016, United States
2 University of Maryland, College Park, MD 20742, United States
     

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LetGbe the Galois group of a solvable Galois extension K/F of number fields. In this note, we demonstrate the holomorphy of certain Artin L-functions attached to K/F, generalizing results of M. R. Murty and A. Raghuram [1]. We also give a bound (generalizing one in [1]) on the orders of certain Artin L-functions at an arbitrary point in the complex plane by the order of a corresponding quotient of Dedekind zeta functions. We deduce some corollaries on the possible orders of zeros of such quotients.
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  • A Variation on the Solvable Case of the Dedekind Conjecture

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Authors

Joshua M. Lansky
American University, Washington, DC 20016, United States
Kevin M. Wilson
University of Maryland, College Park, MD 20742, United States

Abstract


LetGbe the Galois group of a solvable Galois extension K/F of number fields. In this note, we demonstrate the holomorphy of certain Artin L-functions attached to K/F, generalizing results of M. R. Murty and A. Raghuram [1]. We also give a bound (generalizing one in [1]) on the orders of certain Artin L-functions at an arbitrary point in the complex plane by the order of a corresponding quotient of Dedekind zeta functions. We deduce some corollaries on the possible orders of zeros of such quotients.