Pseudodifferential Methods in Number Theory: 13 (Pseudo-Differential Operators) - Softcover

Inhaltsangabe

<P>CLASSICALLY DEVELOPED AS A TOOL FOR PARTIAL DIFFERENTIAL EQUATIONS, THE&NBSP;ANALYSIS OF OPERATORS KNOWN AS PSEUDODIFFERENTIAL ANALYSIS IS HERE REGARDED&NBSP;AS A POSSIBLE HELP IN QUESTIONS OF ARITHMETIC. THE OPERATORS WHICH MAKE UP&NBSP;THE MAIN SUBJECT OF THE BOOK CAN BE CHARACTERIZED IN TERMS OF CONGRUENCE&NBSP;ARITHMETIC.&NBSP;THEY ENJOY A EULERIAN STRUCTURE, AND ARE APPLIED TO THE SEARCH&NBSP;FOR NEW CONDITIONS EQUIVALENT TO THE RIEMANN HYPOTHESIS. THESE CONSIST IN&NBSP;THE VALIDITY OF CERTAIN PARAMETER-DEPENDENT ESTIMATES FOR A CLASS OF HERMITIAN&NBSP;FORMS OF FINITE RANK. THE LITTLEWOOD CRITERION, INVOLVING SUMS OF&NBSP;MÖBIUS COEFFICIENTS, AND THE WEIL SO-CALLED EXPLICIT FORMULA, WHICH LEADS TO&NBSP;HIS POSITIVITY CRITERION, FIT WITHIN THIS SCHEME, USING IN THE FIRST CASE WEYL'S&NBSP;PSEUDODIFFERENTIAL CALCULUS, IN THE SECOND CASE FUCHS'.&NBSP;</P><P>THE BOOK SHOULD BE&NBSP;OF INTEREST TO PEOPLE LOOKING FOR NEW POSSIBLE APPROACHES TO THE RIEMANN&NBSP;HYPOTHESIS, ALSO TO NEW PERSPECTIVES ON PSEUDODIFFERENTIAL ANALYSIS AND ON&NBSP;THE WAY IT COMBINES WITH MODULAR FORM THEORY. ANALYSTS WILL HAVE NO DIFFICULTY WITH THE ARITHMETIC ASPECTS, WITH WHICH, SAVE FOR VERY FEW EXCEPTIONS,&NBSP;NO PREVIOUS ACQUAINTANCE IS NECESSARY.</P>

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.