ON THE ANALYTIC PROPERTIES OF STANDARD ZETA FUNCTIONS OF SIEGEL MODULAR FORMS

1979 ◽  
Vol 35 (1) ◽  
pp. 1-17 ◽  
Author(s):  
A N Andrianov ◽  
V L Kalinin
Keyword(s):  
Modular Forms ◽  
Zeta Functions ◽  
Siegel Modular Forms

scholarly journals p-Adic properties of Siegel modular forms of degree 2

1978 ◽  
Vol 71 ◽  
pp. 43-60 ◽  
Author(s):  
Shōyū Nagaoka
Keyword(s):  
Real Number ◽  
Modular Forms ◽  
Zeta Functions ◽  
Number Fields ◽  
Prime Numbers ◽  
Siegel Modular Forms ◽  
Totally Real

H. P. F. Swinnerton-Dyer determined the structure of the algebra of modular forms mod p for all prime numbers p in elliptic modular case (cf. [10]). Using his result, J.-P. Serre investigated the properties of p-adic modular forms and succeeded to construct the p-adic zeta functions for any totally real number fields (cf. [8]).

Byte weight enumerators and modular forms of genus r

2015 ◽  
Vol 14 (06) ◽  
pp. 1550080
Author(s):  
Anuradha Sharma ◽  
Amit K. Sharma
Keyword(s):  
Modular Forms ◽  
Quadratic Forms ◽  
Zeta Functions ◽  
Siegel Modular Forms ◽  
Type I ◽  
Type Ii ◽  
Jacobi Forms ◽  
Weight Enumerators ◽  
Type Ii Codes ◽  
Real Quaternions

For a positive integer m, let R be either the ring ℤ2m of integers modulo 2m or the quaternionic ring Σ2m = ℤ2m + αℤ2m + βℤ2m + γℤ2m with α = 1 + î, β = 1 + ĵ and [Formula: see text], where [Formula: see text] are elements of the ring ℍ of real quaternions satisfying [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. In this paper, we obtain Jacobi forms (or Siegel modular forms) of genus r from byte weight enumerators (or symmetrized byte weight enumerators) in genus r of Type I and Type II codes over R. Furthermore, we derive a functional equation for partial Epstein zeta functions, which are summands of classical Epstein zeta functions associated with quadratic forms.

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