Theta operators, Goss polynomials, and v-adic modular forms

We investigate hyperderivatives of Drinfeld modular forms and determine formulas for these derivatives in terms of Goss polynomials for the kernel of the Carlitz exponential. As a consequence we prove that v-adic modular forms in the sense of Serre, as defined by Goss and Vincent, are preserved under hyperdifferentiation. Moreover, upon multiplication by a Carlitz factorial, hyperdifferentiation preserves v-integrality.Comment: 20 page

Identities for Anderson generating functions for Drinfeld modules

Anderson generating functions are generating series for division values of points on Drinfeld modules, and they serve as important tools for capturing periods, quasi-periods, and logarithms. They have been fundamental in recent work on special values of positive characteristic L-series and in transcendence and algebraic independence problems. In the present paper we investigate techniques for expressing Anderson generating functions in terms of the defining polynomial of the Drinfeld module and determine new formulas for periods and quasi-periods.Comment: 18 page

An effective criterion for Eulerian multizeta values in positive characteristic

Characteristic p multizeta values were initially studied by Thakur, who defined them as analogues of classical multiple zeta values of Euler. In the present paper we establish an effective criterion for Eulerian multizeta values, which characterizes when a multizeta value is a rational multiple of a power of the Carlitz period. The resulting "t-motivic" algorithm can tell whether any given multizeta value is Eulerian or not. We also prove that if zeta_A(s_1,...,s_r) is Eulerian, then zeta_A(s_2,...,s_r) has to be Eulerian. When r=2, this was conjectured (and later on conjectured for arbitrary r) by Lara Rodriguez and Thakur for the zeta-like case from numerical data. Our methods apply equally well to values of Carlitz multiple polylogarithms at algebraic points and zeta-like multizeta values.Comment: 32 page

Rain in the Valley

Three generations of the Demas family face the ups and downs of the twentieth century after their fathers leave the coal mines that drew them from Greece to America, become wool growers and small businessmen, and Americanize their Demopoulos name. As the years pass, the family accumulates untidy lives and tragedies. Parents seek to keep their children tightly bound by old-country customs, to arrange marriages, and to foist their views of women\u27s inferiority on their daughters. Lia Papastamos in particular, child of a forced marriage between her Greek father and Amerikanidha mother, pulls away from the stifling burden of family tradition and interference, but she and her husband must contend with the decline that time, synthetics, and changing tastes bring to a once-thriving sheep business. Helen Papanikolas was one of Utah\u27s most revered authors. Known and respected nationally and internationally as the preeminent narrator of the Greek American experience, appreciated in Utah particularly for her documentation of our multicultural history, she is widely admired as well for her storytelling through fiction and memoirs. Rain in the Valley, her last book, is a culmination. In a narrative rich with life, insight, and experience she portrays the generations of a Greek-American family. Their story is rooted in sheepherding, set primarily in Helper, Utah, and shaped by the changes that the twentieth century brings to them. Helen Papanikolas is widely known as the preeminent narrator of the Greek American experience. Her ýmonumental contributionsý were honored in 2003 with a special issue of the Journal of the Hellenic Diaspora. Those contributions include Greek and multicultural histories, folklore studies, memoirs, and several works of fiction, including The Time of the Little Black Bird; The Apple Falls from the Apple Tree: Stories; and Small Bird, Tell Me: Stories of Greek Immigrants in Utah. Rain in the Valley was the last work she completed before her death in late 2004.https://digitalcommons.usu.edu/usupress_pubs/1088/thumbnail.jp