LAP Lambert Academic Publishing ( 20170111 )
€ 55,90
LaurentStieltjes constants are the coefficients of the expansion in Laurent series of Dirichlet Lseries. The interest in these constants has a long history (started by Stieltjes in 1885). Among the applications, let us cite : determining zerofree regions for Dirichlet Lfunctions near the real axis in the critical strip, computing the values of Riemann and Hurwitz zeta functions in the complex plane and studying the class number of the quadratic field, etc. In this book, we give explicit upper bounds for LaurentStieltjes constants in the following two cases: The first case when Dirichlet character is fixed and its order goes to infinity, starting from an idea due to Matsuoka for Riemann zeta function. We extend the formula of Matsuoka to Dirichlet Lfunctions, improving previous results. We also deduce an approximation of Dirichlet Lfunctions in the neighborhood of 1 by a short Taylor polynomial. The second case deals more specifically with the first LaurentStieltjes coefficient. We give an improvement of the known explicit upper bounds of this coefficient. This book contains new results about these constants have been published in International journals
Book Details: 

ISBN13: 
9783330029293 
ISBN10: 
3330029293 
EAN: 
9783330029293 
Book language: 
English 
By (author) : 
Sumaia Saad Eddin 
Number of pages: 
148 
Published on: 
20170111 
Category: 
Mathematics 