Titlebook: Quadratic and Higher Degree Forms; Krishnaswami Alladi,Manjul Bhargava,Pham Huu Tiep Book 2013 Springer Science+Business Media New York 20

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On Representation of an Integer by ,, + ,, + ,, and the Modular Equations of Degree 3 and 5,s interesting connections between the properties of this function and certain modular equations of degree 3 and 5. In particular, I show that . follows easily from the well known Ramanujan modular equation of degree 5. Moreover, I establish new relations between .(.) and .(.), .(.), the number of re

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Identifying the Matrix Ring: Algorithms for Quaternion Algebras and Quadratic Forms,determine if a given algebra of rank 4 over a commutative ring . embeds in the 2 ×2-matrix ring M.(.) and, if so, to compute such an embedding. We discuss many variants of this problem, including algorithmic recognition of quaternion algebras among algebras of rank 4, computation of the Hilbert symb

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