Dirichlet series
Noun
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Noun
Dirichlet series
- (number theory) Any infinite series of the form \sum_{n=1}^\infty \frac{a_n}{n^s}, where s and each a_n are complex numbers.
- 2009, Anatoli Andrianov, Introduction to Siegel Modular Forms and Dirichlet Series, Springer (Birkhäuser), page 137 ↗,
- Traditionally, starting from Euler, multiplicativity of arithmetic sequences is customarily expressed in the form of an Euler product factorization of the generating Dirichlet series. It turns out that in the situation of modular forms, suitable Dirichlet series constructed by Fourier coefficients of eigenfunctions of Hecke operators can be expressed through Dirichlet series formed by the corresponding eigenvalues.
- 2012, Daniel Bump, Chapter 1: Introduction: Multiple Dirichlet Series, Daniel Bump, Solomon Friedberg, Dorian Goldfeld (editors), Multiple Dirichlet Series, L-functions and Automorphic Forms, Springer, page 6 ↗,
- We have now given heuristically a large family of multiple Dirichlet series, one for each simply laced Dynkin diagram.
- 2014, Marius Overholt, A Course in Analytic Number Theory, American Mathematical Society, page 157 ↗,
- The sum
- A(s)=\sum_{n=1}^\infty a_n n^{-s}
- of a convergent Dirichlet series is a holomorphic (single-valued analytic) function in the half plane \sigma>\sigma_c(A), and the terms of the Dirichlet series are holomorphic in the whole complex plane, and the series converges uniformly on every compact subset of \sigma>\sigma_c(A) by Proposition 3.3.
- The sum
- 2009, Anatoli Andrianov, Introduction to Siegel Modular Forms and Dirichlet Series, Springer (Birkhäuser), page 137 ↗,
- (infinite series) general Dirichlet series, ordinary Dirichlet series
- Dirichlet L-series
- Italian: serie di Dirichlet
This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.004