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Unification of Chowla’s Problem and Maillet–Demyanenko Determinants

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  • Nianliang Wang

    (College of Applied Mathematics and Computer Science, Shangluo University, Shangluo 726000, China
    To the memory of Professor Dr. Andrzej Schinzel, with great respect.
    These authors contributed equally to this work.)

  • Kalyan Chakraborty

    (KSCSTE-Kerala School of Mathematics, Kozhikode 673571, Kerala, India
    These authors contributed equally to this work.)

  • Shigeru Kanemitsu

    (KSCSTE-Kerala School of Mathematics, Kozhikode 673571, Kerala, India)

Abstract

Chowla’s (inverse) problem (CP) is to mean a proof of linear independence of cotangent-like values from non-vanishing of L ( 1 , χ ) = ∑ n = 1 ∞ χ ( n ) n . On the other hand, we refer to determinant expressions for the (relative) class number of a cyclotomic field as the Maillet–Demyanenko determinants (MD). Our aim is to develop the theory of discrete Fourier transforms (DFT) with parity and to unify Chowla’s problem and Maillet–Demyanenko determinants (CPMD) as different-looking expressions of the relative class number via the Dedekind determinant and the base change formula.

Suggested Citation

  • Nianliang Wang & Kalyan Chakraborty & Shigeru Kanemitsu, 2023. "Unification of Chowla’s Problem and Maillet–Demyanenko Determinants," Mathematics, MDPI, vol. 11(3), pages 1-21, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:655-:d:1049025
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    References listed on IDEAS

    as
    1. N.-L. Wang & Praveen Agarwal & S. Kanemitsu, 2020. "Limiting Values and Functional and Difference Equations," Mathematics, MDPI, vol. 8(3), pages 1-24, March.
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