LARGE MOMENTS AND EXTREME VALUES OF CLASS NUMBERS OF INDEFINITE BINARY QUADRATIC FORMS
Copyright policy )LARGE MOMENTS AND EXTREME VALUES OF CLASS NUMBERS OF INDEFINITE BINARY QUADRATIC FORMS
Let $h(d)$ be the class number of indefinite binary quadratic forms of discriminant $d$, and let $\varepsilon_d$ be the corresponding fundamental unit. In this paper, we obtain an asymptotic formula for the $k$-th moment of $h(d)$ over positive discriminants $d$ with $\varepsilon_d\leq x$, uniformly for real numbers $k$ in the range $0
21 pages. Added a new result (Theorem 1.5) concerning the distribution of large values of the class number. To appear in Mathematika
- Keele University United Kingdom
- University of Toronto Canada
generalized Riemann hypothesis, Mathematics - Number Theory, FOS: Mathematics, Class numbers of quadratic and Hermitian forms, Number Theory (math.NT), indefinite binary quadratic forms, Littlewood conjecture, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]
generalized Riemann hypothesis, Mathematics - Number Theory, FOS: Mathematics, Class numbers of quadratic and Hermitian forms, Number Theory (math.NT), indefinite binary quadratic forms, Littlewood conjecture, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]
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