On values of exponential sums
HTML articles powered by AMS MathViewer
- by Chungming An PDF
- Proc. Amer. Math. Soc. 52 (1975), 131-135 Request permission
Abstract:
An exponential sum is defined by \[ G(F,\varphi ,\alpha ) = \sum \limits _{\gamma \epsilon {{(Z/qZ)}^n}} {\exp (2\pi i(\varphi F(\gamma ) + \langle \alpha ,\gamma \rangle } ))\] for $\varphi = a/q\epsilon Q,\alpha \epsilon {R^n}$, and a positive-definite form $F(x)$ in $n$ variables of degree $\delta$. Its value is studied and the definition is extended to an irrational $\varphi$.References
- Chungming An, On the analytic continuation of a certain Dirichlet series, J. Number Theory 6 (1974), 1–6. MR 330047, DOI 10.1016/0022-314X(74)90002-X
- Chungming An, A generalization of Epstein zeta functions, Michigan Math. J. 21 (1974), 45–48. MR 342470
- J. G. van der Corput, Diophantische Ungleichungen. I. Zur Gleichverteilung Modulo Eins, Acta Math. 56 (1931), no. 1, 373–456 (German). MR 1555330, DOI 10.1007/BF02545780
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 52 (1975), 131-135
- MSC: Primary 10H10; Secondary 10G05
- DOI: https://doi.org/10.1090/S0002-9939-1975-0376561-3
- MathSciNet review: 0376561