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We determine explicit formulas for the number of representations of a positive integer $n$ by quaternary quadratic forms with coefficients $1$, $2$, $5$ or $10$. We use a modular forms approach.
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참고문헌 (21)
참고문헌 신청
A. Alaca / 2007 / Nineteen quaternary quadratic forms / Acta Arith 130(3):277~310
A. Alaca / 2009 / The number of representations of a positive integer by certain quaternary quadratic forms / Int. J. Number Theory 5(1):13~40
A. Alaca / 2007 / On the quaternary forms x2+y2+z2+5t2; x2+y2 +5z2 +5t2 and x2 +5y2 +5z2 +5t2 / JP J. Algebra Number Theory Appl 9(1):37~53
A. Alaca / 2016 / Representations by quaternary quadratic forms with coecients 1, 2, 7 or 14 / Integers 16(A55):16
B. C. Berndt / 2006 / Number Theory in the Spirit of Ramanujan / American Mathematical Society
A. Alaca / 2009 / The number of representations of a positive integer by certain quaternary quadratic forms / Int. J. Number Theory 5(1):13~40
A. Alaca / 2007 / On the quaternary forms x2+y2+z2+5t2; x2+y2 +5z2 +5t2 and x2 +5y2 +5z2 +5t2 / JP J. Algebra Number Theory Appl 9(1):37~53
A. Alaca / 2016 / Representations by quaternary quadratic forms with coecients 1, 2, 7 or 14 / Integers 16(A55):16
B. C. Berndt / 2006 / Number Theory in the Spirit of Ramanujan / American Mathematical Society
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