Part V. Rankin-Selberg method and periods of modular forms

2010 ◽  
pp. 86-114
Author(s):  
Hidenori Katsurada
Keyword(s):  
Modular Forms ◽  
Periods Of Modular Forms

On the periods of modular forms

1977 ◽  
Vol 229 (3) ◽  
pp. 211-221 ◽  
Author(s):  
Goro Shimura
Keyword(s):  
Modular Forms ◽  
Periods Of Modular Forms

scholarly journals On coefficients of Poincaré series and single-valued periods of modular forms

2020 ◽  
Vol 7 (4) ◽  
Author(s):  
Tiago J. Fonseca
Keyword(s):  
Modular Forms ◽  
Fourier Coefficients ◽  
Poincaré Series ◽  
Series Expansions ◽  
Poincare Series ◽  
Integral Weight ◽  
Periods Of Modular Forms

AbstractWe prove that the field generated by the Fourier coefficients of weakly holomorphic Poincaré series of a given level $$\varGamma _0(N)$$ Γ 0 ( N ) and integral weight $$k\ge 2$$ k ≥ 2 coincides with the field generated by the single-valued periods of a certain motive attached to $$\varGamma _0(N)$$ Γ 0 ( N ) . This clarifies the arithmetic nature of such Fourier coefficients and generalises previous formulas of Brown and Acres–Broadhurst giving explicit series expansions for the single-valued periods of some modular forms. Our proof is based on Bringmann–Ono’s construction of harmonic lifts of Poincaré series.

scholarly journals The exceptional zero conjecture for Hilbert modular forms

2009 ◽  
Vol 145 (1) ◽  
pp. 1-55 ◽  
Author(s):  
Chung Pang Mok
Keyword(s):  
Modular Forms ◽  
Hilbert Modular Forms ◽  
Hida Family ◽  
Special Cases ◽  
Hilbert Modular ◽  
Periods Of Modular Forms ◽  
Convolution Method ◽  
Invent Math

AbstractUsing ap-adic analogue of the convolution method of Rankin–Selberg and Shimura, we construct the two-variablep-adicL-function of a Hida family of Hilbert modular eigenforms of parallel weight. It is shown that the conditions of Greenberg–Stevens [R. Greenberg and G. Stevens,p-adic L-functions and p-adic periods of modular forms, Invent. Math.111(1993), 407–447] are satisfied, from which we deduce special cases of the Mazur–Tate–Teitelbaum conjecture in the Hilbert modular setting.

scholarly journals Periods of modular forms and identities between Eisenstein series

2016 ◽  
Vol 367 (1-2) ◽  
pp. 165-183 ◽  
Author(s):  
Kamal Khuri-Makdisi ◽  
Wissam Raji
Keyword(s):  
Eisenstein Series ◽  
Modular Forms ◽  
Periods Of Modular Forms
Sign in / Sign up

Export Citation Format

Share Document