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Analytic Number Theory And Algebraic Asymptotic Analysis

by Jesse Elliott

~~136,37€~~ 122,73€ 10% OFF

 This monograph introduces a unified framework for analyzing and comparing the asymptotic growth of number-theoretic functions through the novel notions of degree and logexponential degree. Extending the asymptotic calculus shaped by du Bois-Reymond, Landau, and Hardy — rooted in notations such as O, o, and ∼ — it provides a formal algebraic language for comparing growth rates, interpreting numerical evidence, and connecting longstanding problems, including the Riemann hypothesis. The new degree formalism incorporates Hardy's logarithmico-exponential functions, built from id, exp, and log using the operations of addition, multiplication, division, and composition, as benchmarks for comparison. The monograph develops foundational results about the structure and algebra of the degree formalism, including its relation to Karamata theory, Hardy fields, transseries, and asymptotic differential algebra. While not offering proofs of major conjectures, it proposes a new way of establishing interdependencies among error terms. Applications to summatory functions, prime gaps, the Riemann zeta function, and Diophantine approximation demonstrate the framework's reach and utility. These applications reduce error terms in analytic number theory to core set of primitives, including the function π(x) — li(x), whose degree equals ½ if and only if the Riemann hypothesis holds.Contents: <ul><li>A Survey of Analytic Number Theory:<ul><li>A Brief History of Primes</li><li>Asymptotic Analysis</li><li>Arithmetic Functions</li><li>Special Functions in Analytic Number Theory</li><li>The Analytic Theory of Primes</li></ul></li><li>Algebraic Asymptotic Analysis:<ul><li>Logexponential Degree</li><li>Asymptotic Algebra</li><li>Asymptotic Continued Fraction Expansions</li></ul></li><li>Applications of Algebraic Asymptotic Analysis to Number Theory:<ul><li>The Prime Counting Function π(x) and Related Functions</li><li>Summatory Functions</li><li>The Riemann Zeta Function ζ(s)</li><li>Primes in Intervals, the nth Prime, and the nth Prime Gap</li><li>Diophantine Approximation and Continued Fractions</li><li>Conjectures</li></ul></li></ul>Readership: Mathematicians or graduate students in mathematics, especially those specializing in analytic number theory or asymtptotic algebra. Sector: academia.
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Recent Progress On Topics Of Ramanujan Sums And Cotangent Sums Associated With The Riemann Hypothesis

by Maier Helmut Maier, Rassias Michael Th Rassias e Toth Laszlo Toth

~~59,63€~~ 47,70€ 20% OFF + 5% CARD

 In this monograph, we study recent results on some categories of trigonometric/exponential sums along with various of their applications in Mathematical Analysis and Analytic Number Theory. Through the two chapters of this monograph, we wish to highlight the applicability and breadth of techniques of trigonometric/exponential sums in various problems focusing on the interplay of Mathematical Analysis and Analytic Number Theory. We wish to stress the point that the goal is not only to prove the desired results, but also to present a plethora of intermediate Propositions and Corollaries investigating the behaviour of such sums, which can also be applied in completely different problems and settings than the ones treated within this monograph.In the present work we mainly focus on the applications of trigonometric/exponential sums in the study of Ramanujan sums — which constitute a very classical domain of research in Number Theory — as well as the study of certain cotangent sums with a wide range of applications, especially in the study of Dedekind sums and a facet of the research conducted on the Riemann Hypothesis. For example, in our study of the cotangent sums treated within the second chapter, the methods and techniques employed reveal unexpected connections with independent and very interesting problems investigated in the past by R de la Bretèche and G Tenenbaum on trigonometric series, as well as by S Marmi, P Moussa and J-C Yoccoz on Dynamical Systems.Overall, a reader who has mastered fundamentals of Mathematical Analysis, as well as having a working knowledge of Classical and Analytic Number Theory, will be able to gradually follow all the parts of the monograph. Therefore, the present monograph will be of interest to advanced undergraduate and graduate students as well as researchers who wish to be informed on the latest developments on the topics treated.
ENGLISH

Number Theory: An Elementary Introduction Through Diophantine Problems

by Duverney Daniel Duverney

~~26,50€~~ 21,20€ 20% OFF + 5% CARD

 Presents an elementary introduction to number theory and its different aspects: approximation of real numbers, irrationality and transcendence problems, continued fractions, diophantine equations, quadratic forms, arithmetical functions and algebraic number theory.
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Topics In Number Theory

by Eie Minking Eie

~~19,81€~~ 15,85€ 20% OFF + 5% CARD

 Covers the theory of modular forms and Jacobi forms of several variables. This book contains the classical theory as well as a theory on Jacobi forms over Cayley numbers developed by the author from 1990 to 2000.
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Hecke'S Theory Of Modular Forms And Dirichlet Series (2nd Printing And Revisions)

by Berndt Bruce C Berndt e Knopp Marvin I Knopp

~~34,45€~~ 27,56€ 20% OFF + 5% CARD

 In 1938, at the Institute for Advanced Study, E Hecke gave a series of lectures on his theory of correspondence between modular forms and Dirichlet series. This book presents his lectures at the University of Illinois at Urbana-Champaign.
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Topics And Methods In Q-Series

by Mc Laughlin James Mc Laughlin

~~82,15€~~ 65,72€ 20% OFF + 5% CARD

 The book provides a comprehensive introduction to the many aspects of the subject of basic hypergeometric series. The book essentially assumes no prior knowledge but eventually provides a comprehensive introduction to many important topics. After developing a treatment of historically important topics such as the q-binomial theorem, Heine's transformation, the Jacobi triple product identity, Ramanujan's 1-psi-1 summation formula, Bailey's 6-psi-6 summation formula and the Rogers-Fine identity, the book goes on to delve more deeply into important topics such as Bailey- and WP-Bailey pairs and chains, q-continued fractions, and mock theta functions. There are also chapters on other topics such as Lambert series and combinatorial proofs of basic hypergeometric identities.The book could serve as a textbook for the subject at the graduate level and as a textbook for a topic course at the undergraduate level (earlier chapters). It could also serve as a reference work for researchers in the area.
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Development Of Elliptic Functions According To Ramanujan

by Venkatachaliengar K Venkatachaliengar

~~37,10€~~ 29,68€ 20% OFF + 5% CARD

 Provides an efficient approach to elliptic functions, based on the ideas of the great Indian mathematician Srinivasa Ramanujan. This book is suitable for graduate students and researchers in Number Theory and Classical Analysis, as well for scholars and aficionados of Ramanujan's work.
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Particle Physics At The Year Of Light - Proceedings Of The Seventeenth Lomonosov Conference On Elementary Particle Physics

256,86€ + 10% CARD

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 Ultrafast spectroscopy is an advanced spectroscopic technique which enables us to capture events (mostly microscopic) in a very rapid time scale (spanning from nanoseconds (10-9 sec) to attosecond (10-18 sec)). The introduction of this spect
ENGLISH

Analytic Number Theory For Undergraduates

by Chan Heng Huat Chan

~~35,78€~~ 28,62€ 20% OFF + 5% CARD

 Suitable for undergraduates who wish to learn some basic results in analytic number theory, this book covers topics such as Bertrand's Postulate, the Prime Number Theorem and Dirichlet's Theorem of primes in arithmetic progression.
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Renaissance Of Asia: Evolving Economic Relations Between South Asia And East Asia - Evolving Economic Relations Between South Asia And East Asia

129,78€ + 10% CARD

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 Suitable for those interested in the economic development of Asia, this book argues that led by the economic dynamism and re-encountering between China and India we are witnessing Asia's re-emergence and re-integration or the Renaissance of Asia.
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Development Of Elliptic Functions According To Ramanujan

by K (.) Venkatachaliengar

95,98€ + 10% CARD

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 Provides an efficient approach to elliptic functions, based on the ideas of the great Indian mathematician Srinivasa Ramanujan. This book is suitable for graduate students and researchers in Number Theory and Classical Analysis, as well for scholars and aficionados of Ramanujan's work.
ENGLISH

Analytic Number Theory For Undergraduates

by Heng Huat (Shandong University, China) Chan

44,61€ + 10% CARD

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 Suitable for undergraduates who wish to learn some basic results in analytic number theory, this book covers topics such as Bertrand's Postulate, the Prime Number Theorem and Dirichlet's Theorem of primes in arithmetic progression.
ENGLISH

Analytic Number Theory For Undergraduates

by Heng Huat (Shandong University, China) Chan

86,52€ + 10% CARD

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 Suitable for undergraduates who wish to learn some basic results in analytic number theory, this book covers topics such as Bertrand's Postulate, the Prime Number Theorem and Dirichlet's Theorem of primes in arithmetic progression.
ENGLISH

Elementary Physical Chemistry

by Bruno (Florida State Univ, Usa) Linder

75,71€ + 10% CARD

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 Suitable for undergraduates, not necessarily chemistry majors, who need to know something about physical chemistry, this book covers the essential topics in physical chemistry, including the state of matter, thermodynamics, chemical kinetics, phase and chemical equilibria, introduction to quantum theory, and molecular spectroscopy.
ENGLISH

Number Theory: An Elementary Introduction Through Diophantine Problems - An Elementary Introduction Through Diophantine Problems

by Daniel (Baggio Engineering School, France) Duverney

87,87€ + 10% CARD

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 Presents an elementary introduction to number theory and its different aspects: approximation of real numbers, irrationality and transcendence problems, continued fractions, diophantine equations, quadratic forms, arithmetical functions and algebraic number theory.
ENGLISH

Topics In Number Theory

by Minking (Nat'L Chung Cheng Univ, Taiwan) Eie

33,80€ + 10% CARD

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 Covers the theory of modular forms and Jacobi forms of several variables. This book contains the classical theory as well as a theory on Jacobi forms over Cayley numbers developed by the author from 1990 to 2000.
ENGLISH

Jacobsthal Sums

by Bogdan (Indiana University Indianapolis, Usa) Nica

~~94,63€~~ 85,17€ 10% OFF

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Analytic Methods In Number Theory: When Complex Numbers Count

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Analytic Methods In Number Theory: When Complex Numbers Count

by Wadim (Radboud Univ, The Netherlands) Zudilin

94,63€ + 10% CARD

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Analytic And Combinatorial Number Theory: The Legacy Of Ramanujan - Contributions In Honor Of Bruce C. Berndt

10%

ENGLISH

Analytic And Combinatorial Number Theory: The Legacy Of Ramanujan - Contributions In Honor Of Bruce C. Berndt

~~236,58€~~ 212,92€ 10% OFF

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Pioneer Merchants Of Singapore, The: Johnston, Boustead, Guthrie And Others

by Richard Edward (-) Hale

148,71€ + 10% CARD

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Topics And Methods In Q-Series

by James (West Chester University, Usa) Mc Laughlin

104,09€ + 10% CARD

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Recent Progress On Topics Of Ramanujan Sums And Cotangent Sums Associated With The Riemann Hypothesis

by Helmut (Univ Of Ulm, Germany) Maier, Laszlo (Univ Of Pecs, Hungary) Toth e Michael Th (Hellenic Military Academy, Greece) Rassias

87,87€ + 10% CARD

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ENGLISH

Modular And Automorphic Forms & Beyond

by Hossein (Inst De Matematica Pura E Aplicada, Brazil) Movasati

135,19€ + 10% CARD

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Biological Shape Analysis - Proceedings Of The 4th International Symposium On Biological Shape Analysis (Isbsa)

235,23€ + 10% CARD

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