scholarly journals Galois families of modular forms and application to weight one

2021 ◽  
Author(s):  
Sara Arias-de-Reyna ◽  
François Legrand ◽  
Gabor Wiese
Keyword(s):  
Modular Forms ◽  
Weight One

scholarly journals The modular equation and modular forms of weight one

1985 ◽  
Vol 100 ◽  
pp. 145-162 ◽  
Author(s):  
Toyokazu Hiramatsu ◽  
Yoshio Mimura
Keyword(s):  
Modular Forms ◽  
Quadratic Field ◽  
Congruence Subgroup ◽  
Algebraic Integer ◽  
Complex Multiplication ◽  
Cusp Forms ◽  
Imaginary Quadratic Fields ◽  
Modular Equation ◽  
Class Invariants ◽  
Weight One

This is a continuation of the previous paper [8] concerning the relation between the arithmetic of imaginary quadratic fields and cusp forms of weight one on a certain congruence subgroup. Let K be an imaginary quadratic field, say K = with a prime number q ≡ − 1 mod 8, and let h be the class number of K. By the classical theory of complex multiplication, the Hubert class field L of K can be generated by any one of the class invariants over K, which is necessarily an algebraic integer, and a defining equation of which is denoted byΦ(x) = 0.

scholarly journals Drinfeld Modular Forms of Weight One

1997 ◽  
Vol 67 (2) ◽  
pp. 215-228 ◽  
Author(s):  
Gunther Cornelissen
Keyword(s):  
Modular Forms ◽  
Drinfeld Modular Forms ◽  
Weight One

The circle method and non-lacunarity of meromorphic modular forms

2015 ◽  
Vol 2015 (703) ◽  
pp. 1-25 ◽  
Author(s):  
Sanoli Gun ◽  
Joseph Oesterlé
Keyword(s):  
Cusp Form ◽  
Modular Forms ◽  
Circle Method ◽  
Weight One

AbstractSerre proved that any holomorphic cusp form of weight one for Γ

scholarly journals Gross–Stark units and p-adic iterated integrals attached to modular forms of weight one

2016 ◽  
Vol 40 (2) ◽  
pp. 325-354 ◽  
Author(s):  
Henri Darmon ◽  
Alan Lauder ◽  
Victor Rotger
Keyword(s):  
Modular Forms ◽  
Iterated Integrals ◽  
Weight One ◽  
Stark Units

scholarly journals Transcendental Nature of Special Values of L-Functions

2011 ◽  
Vol 63 (1) ◽  
pp. 136-152 ◽  
Author(s):  
Sanoli Gun ◽  
M. Ram Murty ◽  
Purusottam Rath
Keyword(s):  
Modular Forms ◽  
Special Values ◽  
Weight One ◽  
Petersson Norms

Abstract In this paper, we study the non-vanishing and transcendence of special values of a varying class of L-functions and their derivatives. This allows us to investigate the transcendence of Petersson norms of certain weight one modular forms.

scholarly journals Petersson inner products of weight-one modular forms

2019 ◽  
Vol 2019 (749) ◽  
pp. 133-159
Author(s):  
Maryna Viazovska
Keyword(s):  
Quadratic Form ◽  
Algebraic Number ◽  
Modular Forms ◽  
Fourier Coefficients ◽  
Theta Series ◽  
Binary Quadratic Form ◽  
Positive Definite ◽  
Arithmetic Properties ◽  
Factorization Formula ◽  
Weight One

Abstract In this paper we study the regularized Petersson product between a holomorphic theta series associated to a positive definite binary quadratic form and a weakly holomorphic weight-one modular form with integral Fourier coefficients. In [18], we proved that these Petersson products posses remarkable arithmetic properties. Namely, such a Petersson product is equal to the logarithm of a certain algebraic number lying in a ring class field associated to the binary quadratic form. A similar result was obtained independently using a different method by W. Duke and Y. Li [5]. The main result of this paper is an explicit factorization formula for the algebraic number obtained by exponentiating a Petersson product.

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