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Bhattacharya, Shubhrajit

University of British Columbia

In this thesis, we establish congruences for values of Dedekind Zeta functions attached to a specific family of totally real fields. Our main theorem generalizes [7, Proposition 2.5]. The proof relies on Iwasawa’s construction of p – adic L– functions and an application of Local Class Field Theory. As a consequence, we derive a criterion for the p – indivisibility of generalized Bernoulli numbers Bn,χ associated with Dirichlet characters χ of p – power order, the triviality of p-torsion in certain even K-groups of specific totally real fields, and congruence modulo p between Euler characteristic of certain arithmetic groups. Our findings demonstrate the applicability of similar methods to establish congruences for Dirichlet L– values at negative odd integers, provided that the corresponding Dirichlet characters satisfy specific congruence criteria modulo a prime p. Our results generalize and offer an alternate approach to some congruences demonstrated in [35].

Text

2025-04-30

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/88086

Mathematics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/