Exact evaluation of second moments associated with some families of curves over a finite field

In this paper, we study moments of Hurwitz class numbers associated to imaginary quadratic orders restricted into fixed arithmetic progressions. In particular, we fix t t in an arithmetic progression t ≡ m ( mod M ) t\equiv m\ \, \left ( \operatorname {mod} \, M \right ) and consider the ratio of the 2 k 2k -th moment to the zeroeth moment for H ( 4 n − t 2 ) H(4n-t^2) as one varies n n . The special case n = p r n=p^r yields as a consequence asymptotic formulas for moments of the trace t ≡ m ( mod M ) t\equiv m\ \, \left ( \operatorname {mod} \, M \right ) of Frobenius on elliptic curves over finite fields with p r p^r elements.

show abstract

Distribution of moments of Hurwitz class numbers in arithmetic progressions and holomorphic projection

Kane

Pujahari

2023

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Exact evaluation of second moments associated with some families of curves over a finite field

Cited by 1 publication

References 8 publications

Distribution of moments of Hurwitz class numbers in arithmetic progressions and holomorphic projection

Distribution of moments of Hurwitz class numbers in arithmetic progressions and holomorphic projection

Contact Info

Product

Resources

About