Journal of the Ramanujan Mathematical Society

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A Note on the Arithmetic Chowla-Milnor Space


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1 Chennai Mathematical Institute, H1 SIPCOT IT Park, Siruseri, Chennai 603 103, India
     

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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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  • A Note on the Arithmetic Chowla-Milnor Space

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Authors

Abhishek T. Bharadwaj
Chennai Mathematical Institute, H1 SIPCOT IT Park, Siruseri, Chennai 603 103, India

Abstract


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.

References