Uniqueness of L-functions and meromorphic functions under sharing of sets
Abhijit Banerjee1 ; Ha Huy Khoai2 ; Arpita Kundu1
1 Department of Mathematics, University of Kalyani, West Bengal India
2 Thang Long Institute of Mathematics and Applied Sciences, Hanoi Vietnam
Journal de théorie des nombres de Bordeaux, Tome 36 (2024) no. 3, pp. 967-985.

In [4], the authors proved that the zero set of a uniqueness polynomial, satisfying some additional conditions, becomes a unique range set for L-functions. They also determined the conditions under which a polynomial becomes a strong uniqueness polynomial for L-functions. These results are the improved version of one result of [3]. In this paper we obtain a number of uniqueness theorems for L-functions in the extended Selberg class, which significantly extend the results of [3] and [4] in a new direction and improve them in some cases. From our results we can show some classes of unique range sets for L-functions which cannot be found by the results of [3] and [4].

Dans [4], les auteurs ont démontré que l’ensemble des zéros d’un polynôme d’unicité, satisfaisant certaines conditions supplémentaires, est un ensemble d’unicité pour les fonctions L. Ils ont également déterminé les conditions sous lesquelles un polynôme est un polynôme d’unicité forte pour les fonctions L. Ces résultats sont une version améliorée d’un résultat de [3]. Dans cet article, nous obtenons un certain nombre de théorèmes d’unicité pour les fonctions L appartenant à la classe de Selberg étendue, qui étendent, de manière significative, les résultats de [3] et [4] dans une nouvelle direction et les améliorons dans certains cas. En utilisant ces résultats, nous pouvons exhiber certaines classes d’ensembles d’unicité pour les fonctions L, qui ne peuvent pas être trouvées avec les résultats de [3] et [4].

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DOI : 10.5802/jtnb.1302
Classification : 11M36, 30D35
Mots-clés : Meromorphic functions, uniqueness, shared sets, small functions, L-functions.

Abhijit Banerjee 1 ; Ha Huy Khoai 2 ; Arpita Kundu 1

1 Department of Mathematics, University of Kalyani, West Bengal India
2 Thang Long Institute of Mathematics and Applied Sciences, Hanoi Vietnam
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Abhijit Banerjee; Ha Huy Khoai; Arpita Kundu. Uniqueness of $L$-functions and meromorphic functions under sharing of sets. Journal de théorie des nombres de Bordeaux, Tome 36 (2024) no. 3, pp. 967-985. doi : 10.5802/jtnb.1302. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1302/

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