Cusp forms of weight one, quartic reciprocity and elliptic curves

DOI10.1017/S0027763000021413zbMath0556.10019OpenAlexW1558953008MaRDI QIDQ3220656

Noburo Ishii

Publication date: 1985

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0027763000021413

zbMATH Keywords

Fourier coefficientsinverse Mellin transformquartic residuequartic reciprocityL-function of elliptic curvehigher reciprocity lawcongruence mod 4cusp form of weight onecusp form of weight twoidentities between cusp formstwo dimensional irreducible complex representationWeil-Langlands theory

Mathematics Subject Classification ID

Elliptic curves (14H52) Congruences for modular and (p)-adic modular forms (11F33) Holomorphic modular forms of integral weight (11F11) Langlands-Weil conjectures, nonabelian class field theory (11R39)

Related Items (10)

On the Dedekind zeta function. II ⋮ Multiplicative Dedekind \(\eta\)-function and representations of finite groups ⋮ Distribution of values of Fourier coefficients for modular forms of weight 1 ⋮ Dedekind \(\eta\)-function in modern research ⋮ Arithmetic properties of Shimura sums related to several modular forms ⋮ The Dedekind eta-function in algebra and number theory: old and new problems ⋮ On the Dedekind zeta function ⋮ On the mean square of the error term for Dedekind zeta functions ⋮ Fourier coefficients of cusp forms and automorphic \(L\)-functions ⋮ Distribution of the roots of a quadratic congruence

Cites Work

• On indefinite modular forms of weight one
• The higher reciprocity laws: An example
• The arithmetic of elliptic curves
• Algorithm for determining the type of a singular fiber in an elliptic pencil
• On Elliptic Curves with Complex Multiplication as Factors of the Jacobians of Modular Function Fields

This page was built for publication: Cusp forms of weight one, quartic reciprocity and elliptic curves