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A page on Eisenstein series in Ramanujan’s lost notebook
- Glasgow Math. J
"... The Eisenstein series in the title, P (q), Q(q), and R(q), are defined by (1.1) P (q): = 1 − 24 (1.2) Q(q): = 1 + 240 ..."
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Cited by 5 (3 self)
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The Eisenstein series in the title, P (q), Q(q), and R(q), are defined by (1.1) P (q): = 1 − 24 (1.2) Q(q): = 1 + 240
KOSHLIAKOV’S FORMULA AND GUINAND’S FORMULA IN RAMANUJAN’S LOST NOTEBOOK
"... Abstract. On two pages in his lost notebook, Ramanujan recorded several theorems involving the modified Bessel function Kν(z). These include Koshliakov’s formula and Guinand’s formula, both connected with the functional equation of nonanalytic Eisenstein series, and both discovered by these authors ..."
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Abstract. On two pages in his lost notebook, Ramanujan recorded several theorems involving the modified Bessel function Kν(z). These include Koshliakov’s formula and Guinand’s formula, both connected with the functional equation of nonanalytic Eisenstein series, and both discovered by these authors several years after Ramanujan’s death. Other formulas, including one by K. Soni and two particularly elegant new results, are stated without proof by Ramanujan. In this paper, we prove all the formulas claimed by Ramanujan on these two pages.
