By Gradimir V. Milovanović, Michael Th. Rassias (eds.)
This ebook, in honor of Hari M. Srivastava, discusses crucial advancements in mathematical examine in a number of difficulties. It includes thirty-five articles, written by way of eminent scientists from the foreign mathematical group, together with either examine and survey works. topics coated comprise analytic quantity concept, combinatorics, specified sequences of numbers and polynomials, analytic inequalities and purposes, approximation of services and quadratures, orthogonality and distinctive and intricate functions.
The mathematical effects and open difficulties mentioned during this publication are provided in an easy and self-contained demeanour. The publication includes an outline of outdated and new effects, equipment, and theories towards the answer of longstanding difficulties in a large clinical box, in addition to new leads to speedily progressing components of analysis. The e-book should be necessary for researchers and graduate scholars within the fields of arithmetic, physics and different computational and utilized sciences.
Read Online or Download Analytic Number Theory, Approximation Theory, and Special Functions: In Honor of Hari M. Srivastava PDF
Best number theory books
"This publication is well-written and the bibliography excellent," declared Mathematical experiences of John Knopfmacher's cutting edge research. The three-part therapy applies classical analytic quantity thought to a wide selection of mathematical matters now not often handled in an arithmetical method. the 1st half offers with arithmetical semigroups and algebraic enumeration difficulties; half addresses arithmetical semigroups with analytical houses of classical sort; and the ultimate half explores analytical homes of different arithmetical platforms.
This monograph relies on learn undertaken via the authors over the last ten years. the most a part of the paintings bargains with homogenization difficulties in elasticity in addition to a few mathematical difficulties on the topic of composite and perforated elastic fabrics. This research of procedures in strongly non-homogeneous media brings forth a good number of only mathematical difficulties that are vitally important for purposes.
The guide Dynamics: Numerical Explorations describes the best way to use this system, Dynamics, to enquire dynamical platforms. Co-author J. A. Yorke, whereas operating with the Maryland Chaos staff, constructed an array of instruments to aid visualize the homes of dynamical platforms. Yorke chanced on it important to mix those quite a few easy instruments with one another right into a unmarried package deal.
- Advanced analytic number theory
- Inducing cuspidal representations from compact opens
- Bernoulli Polynomials
- Equivariant Pontrjagin classes and applications to orbit spaces; applications of the G-signature theorem to transformation groups, symmetric products and number theory
Additional info for Analytic Number Theory, Approximation Theory, and Special Functions: In Honor of Hari M. Srivastava
T / is very strong. T 3=2C" / holds. 3. T 3=2C" / the (hitherto unproved) bound . 2. Let k 2 N be fixed and T =2 6 t 6 2T . Then Z j . 21 C i t/jk log T 1C log2 T log2 T ! j . 21 C i t C iT /jk e jvj dv : (106) Proof. Let D be the rectangle with vertices ˙c ˙ i log2 T , where c D 1= log T . z/dz: (107) D As T ! 1/. By the functional equation (6) and (15) j . 21 c C i t/j j . 21 C c C i t/jT c Since s D 0 is a simple pole of j . s/ 1C log2 T log2 T j . c C jvj/ 1 dv: (109) 40 A. Ivi´c Now set s 0 D s C c C iv D Z 1 1Ci 1 k 2 i C c C i t C iv.
Let k 2 N be fixed and T =2 6 t 6 2T . Then Z j . 21 C i t/jk log T 1C log2 T log2 T ! j . 21 C i t C iT /jk e jvj dv : (106) Proof. Let D be the rectangle with vertices ˙c ˙ i log2 T , where c D 1= log T . z/dz: (107) D As T ! 1/. By the functional equation (6) and (15) j . 21 c C i t/j j . 21 C c C i t/jT c Since s D 0 is a simple pole of j . s/ 1C log2 T log2 T j . c C jvj/ 1 dv: (109) 40 A. Ivi´c Now set s 0 D s C c C iv D Z 1 1Ci 1 k 2 i C c C i t C iv. n/e n s0 n 1: nD1 In the last integral we shift the line of integration to Re w D c and use again the residue theorem and Stirling’s formula.
T 1C" /: nD1 The non-diagonal terms m ¤ n give rise to an expression of the type Z 2T X 1 . , Chap. 2 of ). 1. x/j 6 G in Œa; b. x/e dx ˇ ˇ ˇ a ˇ G=m: (66) 26 A. mn/ 3=4 jn1=2 m1=2 j : " T m¤n6T The contribution of P the remaining terms in (65) is estimated similarly. 2 //1=2 T; where N D T depends on t. T / log2 T . 2 follows if we replace T by T 2 and sum the resulting expressions. T log4 T /: (67) 2 The bound in (67) was obtained independently by Preissman  and the author  in Chap.