Integers represented by positive-definite quadratic forms and Petersson inner products
نویسندگان
چکیده
منابع مشابه
Representations of integers by certain positive definite binary quadratic forms
We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number of solutions to n= x2 +Ny2 for a squarefree integer N .
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There are 65 known positive integers n for which a prime number p prime to D is of the form x2 + ny2 iff p lies in certain congruence classes modulo 4n: these are the idoneal numbers. (It is known that there is at most one further such number and if such a 66th idoneal number exists, then the Generalized Riemann Hypothesis is false.) For n = 1 this is Fermat’s Two Squares Theorem: an odd prime ...
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The level N and squarefree character q of a positive definite ternary quadratic form are defined so that its associated modular form has level N and character Xg ■ We define ä collection of correspondences between classes of quadratic forms having the same level and different discriminants. This makes practical a method for finding representatives of all classes of ternary forms having a given ...
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We consider the problem of classifying all positive-definite integer-valued quadratic forms that represent all positive odd integers. Kaplansky considered this problem for ternary forms, giving a list of 23 candidates, and proving that 19 of those represent all positive odds. (Jagy later dealt with a 20th candidate.) Assuming that the remaining three forms represent all positive odds, we prove ...
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0. Introduction. In [2] it was shown that in a certain sense most integers represented by some form in the genus of a given integral ternary positive definite quadratic form are represented by all forms in this genus. More precisely, let (L,q) be a Zlattice of rank 3 with integral positive definite quadratic form. Then all sufficiently large integers a that are represented primitively by some l...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2019
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa180220-26-9