CONVERGENCE OF DIRICHLET SERIES AND EULER PRODUCTS
نویسندگان
چکیده
منابع مشابه
On Ramanujan and Dirichlet Series with Euler Products
In his unpublished manuscripts (referred to by Birch [1] as Fragment V, pp. 247-249), Ramanujan [3] gave a whole list of assertions about various (transforms of) modular forms possessing naturally associated Euler products, in more or less the spirit of his extremely beautiful paper entitled "On certain arithmetical functions" (in Trans. Camb. Phil. Soc. 22 (1916)). It is simply amazing how Ram...
متن کاملRamanujan identities and Euler products for a type of Dirichlet series
has an Euler product and gave an explicit formulation for the Euler product. In this paper we develop the theory of binary quadratic forms in order to determine the Euler product for ∑∞ n=1 a(n)n −s, and other similarly defined Dirichlet series, in a completely elementary and natural manner. Let N, Z, R and C be the sets of natural numbers, integers, real numbers and complex numbers respectivel...
متن کاملEuler Products and Twisted Euler Products
We describe in brief some aspects of the Langlands program, focussing on Euler products, and also some new constructions, where Euler products are replaced by twisted Euler products. The twisted Euler products are related to automorphic forms on metaplectic groups. 2000 Mathematics Subject Classification: 11F66, 11F55, 11F70, 11M41, 22E55.
متن کاملOn Dirichlet Series and Petersson Products for Siegel Modular Forms
— We prove that the Dirichlet series of Rankin–Selberg type associated with any pair of (not necessarily cuspidal) Siegel modular forms of degree n and weight k > n/2 has meromorphic continuation to C. Moreover, we show that the Petersson product of any pair of square–integrable modular forms of weight k > n/2 may be expressed in terms of the residue at s = k of the associated Dirichlet series....
متن کاملOn the Convergence of the Euler Harmonic Series
The aim oj this article is to study the convergence oj the Euler harmonic series. Firstly, the results concerning the convergence oj the Smaralldache and Erdos harmonic junctions are reviewed Secondly, the Euler harmonic series is proved to be convergent jor a> I, and divergent otherwise. Finally, the slims of the Euler harmonic series are given
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Contributions, Section of Natural, Mathematical and Biotechnical Sciences
سال: 2017
ISSN: 1857-9949,1857-9027
DOI: 10.20903/csnmbs.masa.2017.38.2.111