QFLib package for Pari/GP. C++ routines for local and global computations with integer-valued quadratic forms. These routines compute local densities (at all places) for integer-valued quadratic forms and check representability of all numbers up to a given (multiplicatively defined) bound. These computations produce the explicit (sharp) lower bound for the constant in the asymptotic expression for the ”representation numbers” r_Q(m) described in the 2004 Duke Math. Journal paper of Hanke ”Local Densities and Explicit Bounds for Representability by a Quadratic Form”.
Keywords for this software
References in zbMATH (referenced in 9 articles , 1 standard article )
Showing results 1 to 9 of 9.
- Kim, Kyoungmin; Oh, Byeong-Kweon: Quadratic forms with a strong regularity property on the representations of squares (2020)
- Rouse, Jeremy: Integers represented by positive-definite quadratic forms and Petersson inner products (2019)
- DeBenedetto, Justin; Rouse, Jeremy: Quadratic forms representing all integers coprime to 3 (2018)
- Sardari, Naser T.: Quadratic forms and semiclassical eigenfunction hypothesis for flat tori (2018)
- Sun, Liang: The growth of class numbers of quadratic Diophantine equations (2018)
- Williams, Kenneth S.: Everything you wanted to know about (ax^2+by^2+cz^2+dt^2) but were afraid to ask (2018)
- Lemke Oliver, Robert J.: Representation by ternary quadratic forms (2014)
- Berkovich, Alexander; Hanke, Jonathan; Jagy, Will: A proof of the (S)-genus identities for ternary quadratic forms (2012)
- Hanke, Jonathan: Local densities and explicit bounds for representability by a quadratic form (2004)