New Frontiers in Number Theory and Applications

這本專著介紹了數論及其應用的最新進展和新方向。代數和分析數論是主要的焦點，其中的章節展示了這些領域的快速發展。通過匯集來自七個以上國家的作者，讀者將獲得對當前研究狀態以及可能的研究方向的國際視角。具體涵蓋的主題包括：

- 代數數論
- 橢圓曲線和密碼學
- Hopf Galois 理論
- 分析和初等數論及其應用

《數論與應用的新前沿》將吸引對獲得數論當前研究的全球視角感興趣的研究人員。

Jordi Guàrdia is an associate professor in the Math Department at Universitat Politècnica de Catalunya-Barcelona Tech. His research has been focused in arithmetic geometry and computational number theory. Jointly with J. Montes and E. Nart, he has been involved in the development of Montes algorithm and its theoretical and computational applications, including the Magma package "+Ideals". They are now working in higher rank valuation theory and the interaction between number theory and singularities theory. He is one of the founders of the biannual conference" Jornadas de Teoria de Numeros", and is an active member of the "Seminaride Teoria de Nombres de Barcelona".

Nicuşor Minculete is an associate professor and vice dean at the Faculty of Mathematics and Computer Science, Transilvania University of Brașov, Romania. Nicuşor Minculete's degrees earned: Mathematics at University of Bucharest (1994): Ph.D. in Mathematics at Institute of Mathematics of the Romanian Academy (2012). Research interests: Mathematical Inequalities and its Applications; Number Theory; Euclidean geometry. Member of the Editorial Board at the following journals: European Journal of Mathematics and Applications, International Journal of Geometry, Bulletin of the Transilvania University of Brasov, General Mathematics, Octogon Mathematical Magazine. He has published 100 research papers.

Diana Savin is an associate professor at the Faculty of Mathematics and Computer Science, Transilvania University of Brașov, Romania. Diana Savin graduated from the Faculty of Mathematics and Computer Science of the University of Bucharest in 1996. She obtained the PhD degree in Mathematics at Ovidius University of Constanta, Romania, in 2004, with a thesis about Diophantine equations. Diana Savin works in number theory. Her research directions are algebraic number theory (especially ramification theory in algebraic number fields), associative algebras, computational numbertheory and combinatorics. She wrote several research articles on these areas. Alone or jointly with V. Acciaro, M. Taous and A. Zekhnini, she has been studying quaternion algebras over some algebraic number fields, using ramification theory in algebraic number fields.

Montserrat Vela is an associate professor of the Math Department at Universitat Politècnica de Catalunya-Barcelona Tech. She has worked mainly in the inverse problem in Galois theory, Nowadays, her research is focused on Hopf-Galois theory, having published some relevant papers jointly with T. Crespo and A. Rio. She is an active member of the "Seminari de Teoria de Nombres de Barcelona".

Abdelkader Zekhnini is an associate professor at the Mohammed Premier University, Sciences Faculty, Department of Mathematics, Oujda, Morocco. He obtained the PhD degree in Mathematics in 2014, at the same university with a thesis on capitulation theory and Hilbert class field towers. Before, he was a mathematics teacher in high schools. Abdelkader Zekhnini works in many directions of number theory as algebraic number theory (especialy capitulation theory), Hilbert class field towers, Iwasawa theory, commutative algebra (Integer valued polynomials, Polya fields) and associative algebras. He wrote several research papers on these areas, over 40, published in Web of Science indexed journals.

Jordi Guàrdia是加泰隆尼亞理工大學數學系的副教授。他的研究主要集中在算術幾何和計算數論上。他與J. Montes和E. Nart共同參與了Montes算法的開發，以及該算法在理論和計算應用方面的研究，包括Magma軟件包'+Ideals'。他們目前正在研究高階評價理論以及數論和奇異點理論之間的相互作用。他是雙年會議“Jornadas de Teoria de Numeros”的創辦人之一，也是“巴塞羅那數論研討會”的活躍成員。

Nicușor Minculete是羅馬尼亞布拉索夫特蘭西瓦尼亞大學數學與計算機科學學院的副教授和副院長。他在布加勒斯特大學數學系（1994年）獲得數學學位，並在羅馬尼亞科學院數學研究所（2012年）獲得數學博士學位。他的研究興趣包括數學不等式及其應用、數論和歐幾里得幾何。他是以下期刊的編輯委員會成員：《歐洲數學與應用期刊》、《幾何國際期刊》、《布拉索夫特蘭西瓦尼亞大學公報》、《一般數學》、《八邊形數學雜誌》。他已發表了100篇研究論文。

Diana Savin是羅馬尼亞布拉索夫特蘭西瓦尼亞大學數學與計算機科學學院的副教授。她於1996年畢業於布加勒斯特大學數學與計算機科學學院，並於2004年在康斯坦察奧維迪烏斯大學獲得數學博士學位，論文主題是關於丟番圖方程。Diana Savin從事數論研究，研究方向包括代數數論（尤其是代數數域中的分歧理論）、關聯代數、計算數論和組合數學。她在這些領域撰寫了多篇研究文章。她與V. Acciaro、M. Taous和A. Zekhnini合作研究了一些代數數域上的四元數代數，並使用了代數數域中的分歧理論。

Montserrat Vela是加泰隆尼亞理工大學數學系的副教授。她主要從事Galois理論中的逆問題研究。目前，她的研究重點是Hopf-Galois理論，與T. Crespo和A. Rio合作發表了一些相關論文。她是“巴塞羅那數論研討會”的活躍成員。

Abdelkader Zekhnini是摩洛哥Oujda的穆罕默德一世大學科學學院數學系的副教授。他於2014年在同一所大學獲得數學博士學位，論文主題是關於頭等類塔的投降理論和希爾伯特類域。在此之前，他曾在高中擔任數學教師。Abdelkader Zekhnini從事多個數論方向的研究，包括代數數論（特別是投降理論）、希爾伯特類域、Iwasawa理論、交換代數（整數值多項式、波利亞域）和關聯代數。他在這些領域發表了多篇研究論文，超過40篇，發表在Web of Science索引期刊上。