The characterization of theta functions by functional equations

1995 ◽  
Vol 65 (1) ◽  
pp. 29-55 ◽  
Author(s):  
M. Bonk
Keyword(s):  
Functional Equations ◽  
Theta Functions

scholarly journals Hecke’s modular forms by functional equations

2018 ◽  
Vol 14 (05) ◽  
pp. 1247-1256
Author(s):  
Bernhard Heim
Keyword(s):  
Modular Forms ◽  
Functional Equations ◽  
Hecke Operators ◽  
General Context ◽  
Periodic Functions

We investigate the interplay between multiplicative Hecke operators, including bad primes, and the characterization of modular forms studied by Hecke. The operators are applied on periodic functions, which lead to functional equations characterizing certain eta-quotients. This can be considered as a prototype for functional equations in the more general context of Borcherds products.

scholarly journals To the theory of synchronization of interacting pendulums oscillating in the parallel planes

2020 ◽  
Vol 20 (1) ◽  
pp. 15-37
Author(s):  
S.O. Gladkov ◽  
◽  
S.B. Bogdanova ◽  
Keyword(s):  
Numerical Solution ◽  
Complex Plane ◽  
Nonlinear Dynamic ◽  
Functional Equations ◽  
Electromagnetic Interaction ◽  
Theta Functions ◽  
Addition Theorem ◽  
Physical Factors ◽  
Motion Equations ◽  
Dynamic Motion

The problem of interacting metal pendulums oscillating in parallel planes, the distance $b$ between the suspension points of which is fixed and equally, has been solved. The principle possibility of their synchronization is provided by taking into account two physical factors: 1. Effect of electromagnetic interaction between them and 2. Accounting for EM radiation of each pendulum, leading to non-linear attenuation. The system of nonlinear dynamic motion equations obtained by a strict mathematical path is analyzed, and their numerical solution is given. The article offers a new method for constructing the pairs of function which are holomorphic on the whole complex plane and satisfy functional equations such as the addition theorem for theta functions.

Characterization of field homomorphisms by functional equations, II

2001 ◽  
Vol 62 (1) ◽  
pp. 184-191 ◽  
Author(s):  
F. Halter-Koch ◽  
L. Reich
Keyword(s):  
Functional Equations

scholarly journals Functional equations arisen from the characterization of beta distributions

2009 ◽  
Vol 78 (1-2) ◽  
pp. 87-99 ◽  
Author(s):  
Károly Lajkó ◽  
Fruzsina Mészáros
Keyword(s):  
Functional Equations ◽  
Beta Distributions

scholarly journals On a generalization of Hamburger’s theorem

1985 ◽  
Vol 98 ◽  
pp. 67-76 ◽  
Author(s):  
Akinori Yoshimoto
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Summation Formula ◽  
Number Fields ◽  
Gaussian Field ◽  
Algebraic Number Fields ◽  
Ring Of Integers ◽  
Poisson’S Summation Formula ◽  
The Relationship

The relationship between Poisson’s summation formula and Hamburger’s theorem [2] which is a characterization of Riemann’s zetafunction by the functional equation was already mentioned in Ehrenpreis-Kawai [1]. There Poisson’s summation formula was obtained by the functional equation of Riemann’s zetafunction. This procedure is another proof of Hamburger’s theorem. Being interpreted in this way, Hamburger’s theorem admits various interesting generalizations, one of which is to derive, from the functional equations of the zetafunctions with Grössencharacters of the Gaussian field, Poisson’s summation formula corresponding to its ring of integers [1], The main purpose of the present paper is to give a generalization of Hamburger’s theorem to some zetafunctions with Grössencharacters in algebraic number fields. More precisely, we first define the zetafunctions with Grössencharacters corresponding to a lattice in a vector space, and show that Poisson’s summation formula yields the functional equations of them. Next, we derive Poisson’s summation formula corresponding to the lattice from the functional equations.

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