4 results
ON ALGEBRAIC DIFFERENTIAL EQUATIONS FOR THE GAMMA FUNCTION AND
$L$-FUNCTIONS IN THE EXTENDED SELBERG CLASS
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 96 / Issue 1 / August 2017
- Published online by Cambridge University Press:
- 13 March 2017, pp. 36-43
- Print publication:
- August 2017
-
- Article
-
- You have access
- Export citation
-
This paper concerns the problem of algebraic differential independence of the gamma function and
${\mathcal{L}}$-functions in the extended Selberg class. We prove that the two kinds of functions cannot satisfy a class of algebraic differential equations with functional coefficients that are linked to the zeros of the 
${\mathcal{L}}$-function in a domain 
$D:=\{z:0<\text{Re}\,z<\unicode[STIX]{x1D70E}_{0}\}$ for a positive constant 
$\unicode[STIX]{x1D70E}_{0}$.
UNIQUENESS THEOREMS FOR DIRICHLET SERIES
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 91 / Issue 3 / June 2015
- Published online by Cambridge University Press:
- 12 February 2015, pp. 389-399
- Print publication:
- June 2015
-
- Article
-
- You have access
- Export citation
QUANTUM DEFORMATIONS OF CATALAN’S CONSTANT, MAHLER’S MEASURE AND THE HÖLDER–SHINTANI DOUBLE SINE FUNCTION
-
- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 49 / Issue 3 / October 2006
- Published online by Cambridge University Press:
- 25 January 2007, pp. 667-681
-
- Article
-
- You have access
- Export citation
!ALGEBRAICITY AND TRANSCENDENCY OF BASIC SPECIAL VALUES OF SHINTANI’S DOUBLE SINE FUNCTIONS
-
- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 49 / Issue 2 / June 2006
- Published online by Cambridge University Press:
- 30 May 2006, pp. 361-366
-
- Article
-
- You have access
- Export citation
