In the references[4,11,12],the authors gave some modular forms overΓ^(0)(2).In this note,we proceed with the study of cancellation formulas relating to the modular forms.
In this paper,we study the generalized Dedekind Rademacher sums considered by Hall,Wilson and Zagier.We establish a new formula for the products of two Bernoulli functions by using Parseval's formula,Hurwitz's...In this paper,we study the generalized Dedekind Rademacher sums considered by Hall,Wilson and Zagier.We establish a new formula for the products of two Bernoulli functions by using Parseval's formula,Hurwitz's formula and Lerch's functional equation.As applications of the result,some well-known reciprocity formulas are deduced as special cases.展开更多
Let K_(j)/Q,1≤j≤ν,ν≥2 be quadratic fields with pairwise coprime discriminants Dj,and let τ_(kj)^(K_(j))(n)be the divisor function associated to Dedekind zeta function SK_(j)(s).In this paper,we consider a multid...Let K_(j)/Q,1≤j≤ν,ν≥2 be quadratic fields with pairwise coprime discriminants Dj,and let τ_(kj)^(K_(j))(n)be the divisor function associated to Dedekind zeta function SK_(j)(s).In this paper,we consider a multidimensional general divisor problem related to the τ_(kj)^(K_(j))(n)involving several number fields over square integers,by establishing the corresponding asymptotic formula.As an application,we also obtain the asymptotic formula of variance of these coefi icients.展开更多
文摘In the references[4,11,12],the authors gave some modular forms overΓ^(0)(2).In this note,we proceed with the study of cancellation formulas relating to the modular forms.
基金Supported by the Natural Science Foundation of Sichuan Province(No.2023NSFSC0065)。
文摘In this paper,we study the generalized Dedekind Rademacher sums considered by Hall,Wilson and Zagier.We establish a new formula for the products of two Bernoulli functions by using Parseval's formula,Hurwitz's formula and Lerch's functional equation.As applications of the result,some well-known reciprocity formulas are deduced as special cases.
基金Supported in part by NSFC(Nos.12401011,12201214)National Key Research and Development Program of China(No.2021YFA1000700)+3 种基金Shaanxi Fundamental Science Research Project for Mathematics and Physics(No.23JSQ053)Science and Technology Program for Youth New Star of Shaanxi Province(No.2025ZC-KJXX-29)Natural Science Basic Research Program of Shaanxi Province(No.2025JC-YBQN-091)Scientific Research Foundation for Young Talents of WNU(No.2024XJ-QNRC-01)。
文摘Let K_(j)/Q,1≤j≤ν,ν≥2 be quadratic fields with pairwise coprime discriminants Dj,and let τ_(kj)^(K_(j))(n)be the divisor function associated to Dedekind zeta function SK_(j)(s).In this paper,we consider a multidimensional general divisor problem related to the τ_(kj)^(K_(j))(n)involving several number fields over square integers,by establishing the corresponding asymptotic formula.As an application,we also obtain the asymptotic formula of variance of these coefi icients.
