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Award ID contains: 1700109

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  1. ; ( , Transactions of the American Mathematical Society)
    Let F F be a number field, and n ≥ 3 n\geq 3 be an integer. In this paper we give an effective procedure which (1) determines whether two given quadratic lattices on F n F^n are isometric or not, and (2) produces an invertible linear transformation realizing the isometry provided the two given lattices are isometric. A key ingredient in our approach is a search bound for the equivalence of two given quadratic forms over number fields which we prove using methods from algebraic groups, homogeneous dynamics and spectral theory of automorphic forms. 
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  2. ; ; ( , Journal of Number Theory)
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  3. ; ; ; ( , Israel journal of mathematics)
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  4. ; ( , Advances in mathematics)
    Using dynamics on homogeneous spaces we obtain some new and improved estimates for reduction of indefinite ternary integral quadratic forms. 
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