Unification of Chowla’s Problem and Maillet–Demyanenko Determinants

Nianliang Wang (), Kalyan Chakraborty and Shigeru Kanemitsu
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Nianliang Wang: College of Applied Mathematics and Computer Science, Shangluo University, Shangluo 726000, China
Kalyan Chakraborty: KSCSTE-Kerala School of Mathematics, Kozhikode 673571, Kerala, India
Shigeru Kanemitsu: KSCSTE-Kerala School of Mathematics, Kozhikode 673571, Kerala, India

Mathematics, 2023, vol. 11, issue 3, 1-21

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.

Keywords: class number formula; discrete Fourier transform; Dedekind determinant; Hurwitz zeta function; Lerch zeta function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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