Multiplicative p-adic metric Diophantine approximation on manifolds and dichotomy of exponents

2020 ◽  
Vol 148 (4) ◽  
pp. 733-747
Author(s):  
Shreyasi Datta ◽  
Anish Gosh
Keyword(s):  
Diophantine Approximation ◽  
Metric Diophantine Approximation

scholarly journals Metric Diophantine approximation with congruence conditions

2020 ◽  
Vol 16 (09) ◽  
pp. 1923-1933
Author(s):  
Erez Nesharim ◽  
René Rühr ◽  
Ronggang Shi
Keyword(s):  
Ergodic Theorem ◽  
Diophantine Approximation ◽  
Congruence Subgroup ◽  
Weighted Approximation ◽  
Simple Approximation ◽  
Rational Approximations ◽  
Congruence Condition ◽  
Metric Diophantine Approximation ◽  
Congruence Classes

We prove a version of the Khinchin–Groshev theorem for Diophantine approximation of matrices subject to a congruence condition. The proof relies on an extension of the Dani correspondence to the quotient by a congruence subgroup. This correspondence together with a multiple ergodic theorem are used to study rational approximations in several congruence classes simultaneously. The result in this part holds in the generality of weighted approximation but is restricted to simple approximation functions.

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