Modular Functions in Analytic Number Theory (Markham Mathematics Series)
12 Angebote vergleichen

Lieferung aus: Vereinigtes Königreich Großbritannien und Nordirland, in-stock.
Knopp's engaging book presents an introduction to modular functions in number theory by concentrating on two modular functions, $\eta(\tau)$ and $\vartheta(\tau)$, and their applications to two number-theoretic functions, $p(n)$ and $r s(n)$. They are well chosen, as at the heart of these particular applications to the treatment of these specific number-theoretic functions lies the general theory of automorphic functions, a theory of far-reaching significance with important connections to a great many fields of mathematics. The book is essentially self-contained, assuming only a good first-year course in analysis. The excellent exposition presents the beautiful interplay between modular forms and number theory, making the book an excellent introduction to analytic number theory for a beginning graduate student. Table of Contents: The Modular Group and Certain Subgroups: 1. The modular group; 2. A fundamental region for $\Gamma(1)$; 3. Some subgroups of $\Gamma(1)$; 4. Fundamental regions of subgroups. Modular Functions and Forms: 1. Multiplier systems; 2. Parabolic points; 3 Fourier expansions; 4. Definitions of modular function and modular form; 5. Several important theorems. The Modular Forms $\eta(\tau)$ and $\vartheta(\tau)$: 1. The function $\eta(\tau)$; 2. Several famous identities; 3. Transformation formulas for $\eta(\tau)$; 4. The function $\vartheta(\tau)$. The Multiplier Systems $\upsilon {\eta}$ and $\upsilon {\vartheta}$: 1. Preliminaries; 2. Proof of theorem 2; 3. Proof of theorem 3. Sums of Squares: 1. Statement of results; 2. Lipschitz summation formula; 3. The function $\psi s(\tau)$; 4. The expansion of $\psi s(\tau)$ at $-1$; 5. Proofs of theorems 2 and 3; 6. Related results. The Order of Magnitude of $p(n)$: 1. A simple inequality for $p(n)$; 2. The asymptotic formula for $p(n)$; 3. Proof of theorem 2. The Ramanujan Congruences for $p(n)$: 1. Statement of the congruences; 2. The functions $\Phi {p,r}(\tau)$ and $h p(\tau)$; 3. The function $S.

Lieferung aus: Vereinigte Staaten von Amerika, Usually ships in 1-2 business days.
Von Händler/Antiquariat, Brooke Books.
From the Preface: "An accurate (though uninspiring) title for this book would have been Applications of the Theory of the Modular Forms $\eta(\tau)$ and $\vartheta(\tau)M$ to the Number-Theoretic functions $p(n)$ and $r_s(n)$ respectively. This is accurate because, except in the first two chapters, we deal exclusively with these two modular forms and these two number-theoretic functions. However, at the heart of these particular applications to the treatment of these specific number-theoretic functions lies the general theory of automorphic functions, a theory of far-reaching significance with important connections to a great many fields of mathematics. Indeed, together with Riemann surface theory, analytic number theory has provided the principal impetus for the development over the last century of the theory of automorphic functions ... I have tried to keep the book self-contained for those readers who have had a good first-year graduate course in analysis; and, in particular, I have assumed readers to be familiar with the Cauchy theory and the Lebesgue theorem of dominated convergence.", Hardcover, Label: Markham Pub. Co, Markham Pub. Co, Produktgruppe: Book, Publiziert: 1970, Studio: Markham Pub. Co, Verkaufsrang: 3690198.

Von Händler/Antiquariat, HPB-Ohio [56525498], Dallas, TX, U.S.A.
Item may show signs of shelf wear. Pages may include limited notes and highlighting. Includes supplemental or companion materials if applicable. Access codes may or may not work. Connecting readers since 1972. Customer service is our top priority.

Lieferung aus: Vereinigte Staaten von Amerika, plus shipping, Shipping area: DOM.
Von Händler/Antiquariat, HPB-Ohio, OH, Columbus, [RE:4].
Item may show signs of shelf wear. Pages may include limited notes and highlighting. Includes supplemental or companion materials if applicable. Access codes may or may not work. Connecting readers since 1972. Customer service is our top priority. Hardcover, 2nd ed.

Lieferung aus: Vereinigte Staaten von Amerika, Usually ships in 1-2 business days, Real shipping costs can differ.
Von Händler/Antiquariat, Chris's Bargains.
From the Preface: "An accurate (though uninspiring) title for this book would have been Applications of the Theory of the Modular Forms $\eta(\tau)$ and $\vartheta(\tau)M$ to the Number-Theoretic functions $p(n)$ and $r_s(n)$ respectively. This is accurate because, except in the first two chapters, we deal exclusively with these two modular forms and these two number-theoretic functions. However, at the heart of these particular applications to the treatment of these specific number-theoretic functions lies the general theory of automorphic functions, a theory of far-reaching significance with important connections to a great many fields of mathematics. Indeed, together with Riemann surface theory, analytic number theory has provided the principal impetus for the development over the last century of the theory of automorphic functions ... I have tried to keep the book self-contained for those readers who have had a good first-year graduate course in analysis; and, in particular, I have assumed readers to be familiar with the Cauchy theory and the Lebesgue theorem of dominated convergence.", Hardcover, Edition: 2nd, Label: American Mathematical Society, American Mathematical Society, Product group: Book, Published: 2003-01-01, Release date: 2003-01-01, Studio: American Mathematical Society, Sales rank: 6577576.

Von Händler/Antiquariat, Murray Media [59705792], North Miami Beach, FL, U.S.A.
Great condition with minimal wear, aging, or shelf wear.

Lieferung aus: Vereinigte Staaten von Amerika, Versandkosten nach: USA.
Von Händler/Antiquariat, Zubal Books.
Markham Publishing Company, 1970. 150 pp., Hardcover, corners rubbed, else very good.

Von Händler/Antiquariat, Zubal-Books [581], Cleveland, OH, U.S.A.
150 pp., Hardcover, corners rubbed, else very good.

Von Händler/Antiquariat, Antiquariat Wirthwein - Die Wortfreunde [6764574], Mannheim, Germany.
154 Seiten Sehr gutes frisches Exemplar. Sprache: Englisch Gewicht in Gramm: 472, Books.

Lieferung aus: Vereinigte Staaten von Amerika, zzgl. Versandkosten, Verandgebiet: DOM.
Von Händler/Antiquariat, More Books, FL, MIAMI, [RE:3].
Hardcover.