Dedekind η-function and indefinite quadratic forms
Copyright policy )Dedekind η-function and indefinite quadratic forms
The author investigates some special theta series with the property \(\Theta (\tau)=\nu \eta^ d(\tau)\). Here \(\eta (\tau)\) is the Dedekind \(\eta\)-function, \(\nu\) is a constant. The author extends the method of the paper [\textit{A. G. van Asch}, Math. Ann. 222, 145--170 (1976; Zbl 0329.10017)] and discovers a new set of examples of such theta series. These examples are connected with indefinite quadratic forms \(S(x\oplus y)=g_ 1 S_ 1(x)-g_ 2 S_ 2(y)\) where \(g_ i\) is a coefficient and \(S_ i\) is a quadratic form defined by some finite root system, \(i=1,2\).
theta series, Analytic theory (Epstein zeta functions; relations with automorphic forms and functions), Dedekind eta function, Dedekind sums, indefinite quadratic forms, finite root system, indefinite, Dedekind eta-function, quadratic forms
theta series, Analytic theory (Epstein zeta functions; relations with automorphic forms and functions), Dedekind eta function, Dedekind sums, indefinite quadratic forms, finite root system, indefinite, Dedekind eta-function, quadratic forms
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