Nineteen quaternary quadratic forms

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Publication:5429111

DOI10.4064/aa130-3-5zbMath1131.11025OpenAlexW2133974350MaRDI QIDQ5429111

Mathieu Lemire, Şaban Alaca, Kenneth S. Williams, Ayşe Alaca

Publication date: 29 November 2007

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/aa130-3-5




Related Items (34)

Unnamed ItemRepresentations of integers by certain \(2k\)-ary quadratic formsFOURIER SERIES OF A CLASS OF ETA QUOTIENTSAnalogues of the Ramanujan-Mordell theoremFOURTEEN OCTONARY QUADRATIC FORMSOn the number of representations of a positive integer as a sum of two binary quadratic formsUnnamed ItemFormulas for cubic partition with 3-coresSome arithmetic convolution identitiesEvaluation of the convolution sums ∑l+36m=n σ(l)σ(m) and ∑4l+9m=n σ(l)σ(m)Unnamed ItemCombinatorial proofs of five formulas of LiouvilleQuartic congruences and eta productsRepresentations of Bell-type quaternary quadratic formsSome Formulas of Liouville in the Spirit of GaussJACOBI'S THETA FUNCTIONS AND THE NUMBER OF REPRESENTATIONS OF A POSITIVE INTEGER AS A SUM OF FOUR TRIANGULAR NUMBERSA result similar to Lagrange's theoremOn the number of representations of n as a linear combination of four triangular numbers IIRepresentations by quaternary quadratic forms whose coefficients are 1, 4, 9 and 36Unnamed ItemThe power series expansion of certain infinite products \newline \(q^{r}\prod_{n=1}^{\infty}(1-q^{n})^{a_{1}}(1-q^{2n})^{a_{2}}\cdots(1-q^{mn})^{a_{m}}\)Unnamed ItemINFINITE FAMILIES OF CONGRUENCES FOR OVERPARTITIONS WITH RESTRICTED ODD DIFFERENCESON THE REPRESENTATIONS OF INTEGERS BY CERTAIN QUADRATIC FORMSProofs of some conjectures of Z.-H. Sun on relations between sums of squares and sums of triangular numbersTheta products and eta quotients of level 24 and weight 2THE REPRESENTATION NUMBERS OF THREE OCTONARY QUADRATIC FORMSEvaluation of some \(q\)-integrals in terms of the Dedekind eta functionA numerical study on exceptional eigenvalues of certain congruence subgroups of \(\mathrm {SO}(n,1)\) and \(\mathrm {SU}(n,1)\)The number of representations of n as a linear combination of triangular numbersUnnamed ItemSome relations between $t(a,b,c,d;n)$ and $N(a,b,c,d;n)$Relations among representations of integers by certain quadratic formsON THE QUATERNARY FORMS x2+y2+2z2+3t2, x2+2y2+2z2+6t2, x2+3y2+3z2+6t2 AND 2x2+3y2+6z2+6t2




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