Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Equidistribution on homogeneous spaces and the distribution of approximates in Diophantine approximation


Authors: Mahbub Alam and Anish Ghosh
Journal: Trans. Amer. Math. Soc. 373 (2020), 3357-3374
MSC (2010): Primary 37A17; Secondary 11K60
DOI: https://doi.org/10.1090/tran/7997
Published electronically: February 11, 2020
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The present paper is concerned with equidistribution results for certain flows on homogeneous spaces and related questions in Diophantine approximation. First, we answer in the affirmative, a question raised by Kleinbock, Shi, and Weiss regarding equidistribution of orbits of arbitrary lattices under diagonal flows and with respect to unbounded functions. We then consider the problem of Diophantine approximation with respect to rationals in a fixed number field. We prove a number field analogue of a famous result of W. M. Schmidt which counts the number of approximates to Diophantine inequalities for a certain class of approximating functions. Further we prove ``spiraling'' results for the distribution of approximates of Diophantine inequalities in number fields. This generalizes the work of Athreya, Ghosh, and Tseng as well as Kleinbock, Shi, and Weiss.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 37A17, 11K60

Retrieve articles in all journals with MSC (2010): 37A17, 11K60


Additional Information

Mahbub Alam
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Mumbai, 400005 India
Email: mahbub@math.tifr.res.in

Anish Ghosh
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Mumbai, 400005 India
Email: ghosh@math.tifr.res.in

DOI: https://doi.org/10.1090/tran/7997
Received by editor(s): February 18, 2019
Received by editor(s) in revised form: August 23, 2019
Published electronically: February 11, 2020
Additional Notes: The second author was supported by a grant from the Indo-French Centre for the Promotion of Advanced Research; a Department of Science and Technology, Government of India Swarnajayanti fellowship and a MATRICS grant from the Science and Engineering Research Board.
Article copyright: © Copyright 2020 American Mathematical Society