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Milnor, motivated by a work of P. Chowla and S. Chowla, formulated a conjecture about linear independence of some special Hurwitz zeta values over the field of rational numbers. In [7,8], Gun, et al. derived non-trivial lower bounds of the dimension of the space generated by these Hurwitz zeta values over certain family of number fields. This they did by working with a natural subspace. In this note, we study the dimensions of these canonical subspaces over any arbitrary number field.

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References

A. Baker, Transcendental number theory, Cambridge Mathematical Library, Cambridge University Press, Cambridge, Second edition (1990).

J. W. S. Cassels, Footnote to a note of Davenport and Heilbronn, J. Lond. Math. Soc., 36 (1961) 177–184.

T. Chatterjee, S. Gun and P. Rath, A number field extension of a question of Milnor, Contemp. Math., 655 (2015) 15–26.

P. Chowla and S. Chowla, On irrational numbers, Norske Vid. Selsk. Skr. (Trondheim), 3 (1982) 15.

H. Davenport and H. A. Heilbronn, On the zeros of certain Dirichlet series, Proc. Lond. Math. Soc., 11 (1936), 181–185.

K. Girstmair, Letter to the editor, J. Number Theory, 23 no. 3, (1986) 405.

S. Gun, M. Ram Murty, and P. Rath, On a conjecture of Chowla and Milnor, Canad. J. Math., 63(6) (2011), 1328–1344.

S. Gun, M. Ram Murty and P. Rath, Linear independence of Hurwitz zeta values and a theorem of Baker-Birch-Wirsing over number fields, Acta Arith., 155 no. 3, (2012) 297–309.

J. Milnor, On polylogarithms, Hurwitz zeta functions, and the Kubert identities, Enseign. Math. (2), 29(3–4) (1983) 281–322.

T. Okada, On a theorem of S. Chowla, J. Number Theory, 2 (1970) 120–123.

T. Okada, On a certain infinite series for a periodic arithmetical function, Acta Arith., 40(2) (1981/82), 143–153.

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