Effective bounds for traces of singular moduli
نویسندگان
چکیده
منابع مشابه
Traces of Singular Moduli
Introduction. “Singular moduli” is the classical name for the values assumed by the modular invariant j(τ) (or by other modular functions) when the argument is a quadratic irrationality. These values are algebraic numbers and have been studied intensively since the time of Kronecker and Weber. In [5], formulas for their norms, and for the norms of their differences, were obtained. Here we obtai...
متن کاملIdentities for Traces of Singular Moduli
Abstract. Generalizing work of Zagier, in an important recent paper Bruinier and Funke prove that the generating functions for traces of singular values of many modular functions are weight 3 2 modular forms. Using facts about half-integral weight modular forms, we obtain identities relating traces of singular moduli for modular functions of level p and 1. These follow from a general result rel...
متن کاملCongruences for Traces of Singular Moduli
We extend a result of Ahlgren and Ono [1] on congruences for traces of singular moduli of level 1 to traces defined in terms of Hauptmodul associated to certain groups of genus 0 of higher levels.
متن کاملSome Congruences for Traces of Singular Moduli
We address a question posed by Ono [7, Problem 7.30], prove a general result for powers of an arbitrary prime, and provide an explanation for the appearance of higher congruence moduli for certain small primes. One of our results overlaps but does not coincide with a recent result of Jenkins [6]. This result essentially coincides with a recent result of Edixhoven [3], and we hope that the compa...
متن کاملKloosterman Sums and Traces of Singular Moduli
where q = e. Let d ≡ 0, 3 (mod 4) be a positive integer, so that −d is a negative discriminant. Denote by Qd the set of positive definite integral binary quadratic forms Q(x, y) = ax + bxy + cy = [a, b, c] with discriminant −d = b − 4ac, including imprimitive forms (if such exist). We let αQ be the unique complex number in the upper half plane H which is a root of Q(x, 1) = 0. Values of j at th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2020
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2019.12.011