Local-Global Results Information

For quadratic forms - representing a number

• Tartakowsky (n>=5) -- circle method
• Kloosterman (n=4) -- circle method
• Duke-SP (n=3) -- modular forms and the Shimura lift
• SP (n=3) -- Arithmetic Method
• Hanke (n=3)-- modular forms and the Shimura lift

Forms by forms

• Hsia-Kneser-Kitaoka (???) -- Arithmetic methods
• Kitaoka (???) -- Siegel modular forms
• Ellenberg-Venkatesh (n >= m+2 > 5) -- Ergodic Theory

Survey Papers

• Sarnak
• Iwaniec
• Duke
• Hanke
• SP